As noted elsewhere, both the Fedorks and the Parodians are incredibly screwed-up societies. What's interesting is that both of them got that way for the same reason: Neither is held responsible for the consequences of their actions. If it weren't for the influence of Cue, the Fedorks would have to come up with at least a vaguely functional social structure or they'd all blow up and/or starve to death. And Quentin himself notes that if Galacti-Transit had had to deal either with market realities (like a proper business) or some level of true public direction (like a proper government department), then the screwed-up mess of The Coldest Equation could never have happened.
The entire Federation:
The Cosmic Being that keeps the Federation in working order keeps an entire race under the delusion that they are not Too Dumb to Live; An entire race has been reduced to some Cosmic Being's pet gold fish.
Alternately, the Federation is hiding behind the protection of that Cosmic Being so they don't have to change elements of their civilization that are just plain broken.Which is just about everything.
Or: An entire species that is just too idiotic to realize that, when a Nigh Invulnerable, God-like, cosmic entity with unimaginable wisdom at it's disposal tells you that you really need to make some changes to the way they have been doing things, you should probably do so. The Cosmic Being literally devotes nearly all of it's spare time just to keeping their absolute mess of a government/educational system/legal system/EVERY FREAKIN' POSSIBLE FACET OF THEIR SOCIETY AND CULTURE from collapsing in a fiery heap of shame and failure. Again. The only change that has occurred in their society in 400 years of interstellar exploration is that the smart ones actually have an opportunity to leave their steaming failure of a society before it finally self destructs.
The scariest thing about the entire scenario is that, the higher up the command chain you go, the greater the incompetence of the people in charge. Looking at the crew of the Glorious Undertaking, and their entire civilization, is like looking at the The Dilbert Principle in action: the most incompetent people have been elevated to the highest offices, while the most competent are stuck at the lowest levels. This is most likely due to the fact that those who support the flawed ideals of the ruling regime are the ones who decide who gets promoted, so those who support the ruling regime are the only ones who get promoted. And since only an incompetent idiot would fail to see that the system is not working, only incompetent idiots get promoted. Meanwhile, the failing system is held together by the incredibly competent people who spend their entire lives at the bottom of the ladder.
The crew of the Glorious Undertaking sit idly by and watch as a comet strikes a planet full of sapient (but Bronze Age tech level) sophonts. They made no effort to aid, evacuate, or rescue the inhabitants... and they cite the Prime Directive as the reason why they didn't make a move to aid anyone. Now, feel free to go try and watch any episode of Star Trek: The Next Generation where The Prime Directive is a major theme without cringing, because this very closely mirrors more than one episode where the Prime Directive hindered the crew of the Enterprise in helping less advanced races in surviving situations that would be an extinction level event.
The Coldest Equations chapter takes all of the fridge horror of The Cold Equations story, and turns it into a court case: What kind of a society would impose a death sentence penalty for stowing away on shuttles with zero security, allows literally no margin of error for said shuttles, and cut the shuttle's operating parameters to the point that there literally wasn't even room for a co-pilot? The space shuttles used by the Parodians would not, by 20th century standards, be cleared for flight about 1,000 feet!
More on the What kind of company would make such a Death trap in The Coldest Equations? Dilbert's company would make such a death trap. Take a close look at the Transit.General., Doesn't he look like the Pointy-haired boss? It also shows just what kind of damage a company like Dilbert's could do for money.
Though Gal-Tech is not an independent corporation. It's federalized. The "boss" in question is the Transportation General, a government official and something akin to the Attorney or Surgeon General. Basically what you're looking at here is the transportation equivalent of the communist Great Leap Forward.
In addition, it certainly explains how such a law about stowing away would come into existence, not to mention why refusal to space the stowaway would be considered to be conspiracy to commit piracy.
The fact that Galacti-Transit is Federalized means the Parodian Government itself is the Dilbert Company which just makes it even worse.
More worrying is this: they've been part of the empire for 50 years, at least, and the Empire has been exercising a hands off policy regarding the running of their world... which, as we can see, has meant that they've had the opportunity to improve, but have willingly chosen not to. This isn't incompetence, it's intentional obstruction of progress: Zero Point Energy would put a lot of fuel producers (such as the ones who mine Decimite crystals) out of business. It is, in a way, like how modern society has access to vast numbers of alternative fuel sources, yet the current fuel companies (big oil, coal, etc) will continue to hinder the use of these alternatives, even though the majority of those alternatives are cheap and limitless, and the current versions are costly and severely limited. Long story short, the ones in charge have been staying the course in order to keep lining their pockets with wealth, while the average citizen is oppressed by laws made specifically to hold the status quo.
And it gets worse: there are, on top of everything else, 2,134 "safety regulations" on the shuttles in question, meaning that any violation would, in fact, be considered "Operator Error". As one character puts it, it is physically impossible for anyone outside of a dedicated artificial intelligence to obey all of those regulations at any given time, let alone remember all of them. And it is also pointed out that those regulations are the exact reason why the shuttles are a screaming metal death trap.
It's finally revealed that the reason for all of this is due to a runaway government bureaucracy that is so divorced from the consequences of it's actions that it can get away with reckless disregard for the lives of the individuals they are supposed to be helping... up until a much higher authority decides that the situation is so bad the only sane response is to shut down the entire agency, lock, stock, and barrel.
Unsurprisingly, considering his biases, the author has it exactly backwards - safety regulations exist because, unless made to do otherwise by some higher authority, private companies in real life will and have failed to implement even basic safety measures in favor of reducing operating costs and increasing profit. Some have even been found to have considered the matter and decided it's less expensive overall to let a certain number of people die every year, and only to pay to clean up the "messes" when they happen (and someone sues), rather than prevent them in the first place. Just as the original story being criticized bends over backwards to create an improbable no-win situation to deliver its Anvilicious moral, so does this one contrive to have a government bureaucracy act exactly like unregulated private industry has shown, time and again, it will when allowed.
To the contrary, however (and as pointed out by the AI prosecuting attorney), the point is not malice, but incompetence. Galacti-Transit is a private company being operated by the government, and governments tend to be very, very bad at running private companies. The "safety regulations" in question, for example, were part environmental (the stripped-to-nothing shuttles were very eco-friendly) and part technological (could not use any technology not thoroughly approved by the government). The government's intent was to run a good emergency shuttle service; they were simply incapable of doing so within the regulations they enacted. (For a real-life comparison, ambulances in England are government-run; it was found that government regulations were actually lowering chances of survival by allowing only one minute for the paramedics to evaluate a patient.)
Also, look up the Brewster F2A Buffalo, the M16 rifle, and the Bradley Fighting Vehicle - all so horribly defective that there was only one possible buyer, one which not only bought countless numbers but asked for them to be built in the first place; The Government. In the case of the deathtrap shuttle? They asked for something cheap and environmentally friendly which could be built, maintained, and supplied solely by low-bid government contractors. Leave out the "cheap" and "environmentally friendly" parts and that's the design statement of NASA's Shuttle Transportation System.