"Here the story should really end, for, in real life, the forlorn old man would have little to look forward to but death. The author took pity on him and has provided a quite improbable epilogue."
— Only text displayed in the silent film The Last Laugh (Der letzte Mann).
That's the whole point of Doctor Who in these narrative collapse stories - that ultimately there is no such thing as threatening the fundamental narrative logic of Doctor Who because, eventually, it just shrugs its shoulders and does something random to get out of it.
There's Plot Convenience, there's Deus ex Machina, and then there's just pulling stuff right out of your ass! THAT... CAN'T... HAPPEN!!! You can't just go filling plot holes with bullshit! I've had acid flashbacks who had more narrative coherence than this!
"Akiha...? What do you mean by Nee-san?"
"I mean Nee-san. Now that I think about it, I had a twin older sister...!"
"You had an older sister... that's a bit of a sudden statement."
Even though this is a parody, this is too much. It's no fun if you don't lay down any groundwork or foreshadowing.
"I don't care about that...!"
— Kagetsu Tohya, ("Imogirisou")
We were invited to the island
All our friends were to be there
A party for the ages
Everyone without a care
But storm clouds came from nowhere...
— Parry Gripp, "Me and You and Pikachu"
"A hawk summon, where did he get that?"
— Tobi/Obito (pretending to be Madara), Naruto
"Think about it! What you've done is utterly ridiculous! And that's saying something in a world where people can make water dragons using sign language!"
"Think of it this way: At least you didn't have to reach in and pull it out. Poor Andrew."
Fake Kidnapper: Come on, get in the trunk!
George: What about my ankle monitor?
Fake Kidnapper: We have an ankle monitor deactivator!
George: Oh, good. See, I've been meaning to get one of those...
"So, lemme see if I understand this: Prometheus said he didn't know who the Shade was, but apparently the device he had planted was specifically designed to counteract his powers. What a convenient device! Oh, and the super-duper-maxi-extreme-ultra devices can counteract the magic of the REAL Captain Marvel too. Look, there's smart villains, clever planning, and then there's just pulling crap outta your ass!"
-Thou Shalt Set Up Plot Twists Appropriately
I feel giving any examples will be unacceptable spoilerage, so let me just briefly say that 'support character was evil all along' does NOT constitute 'character development.' What that is is 'arse pull.'