WMG: Indiana Jones and the Kingdom of the Crystal Skull

The Two FBI agents blacklisting Indy were double agents covering their own ass.
Why else would they be there conveniently to accuse Indiana of treason? Plus Indy subtly accused them of such a crime.
FBI: Don't wave your war record in our face Colonel Jones. We all served.
Jones: No kidding. Which side were you on?
  • This was during the Red Scare. Need I say more?

Indy's friend, General Ross, is 'Thunderbolt' Ross's father
Alternatively, General Ross from Crystal Skull is General ‘Thunderbolt’ Ross’ grandfather. Also, Indy’s General Ross had at least two children, a son and a daughter, the son being Thunderbolt’s father. The daughter married a man with the last name of Rockwell and they also had son who grew up to be a high ranking member of the World Security Council, who happens to be an Identical Grandson to the elder General Ross.

The reason for Nuking The Fridge working...
Shiva, God and Christ owed him one for protecting the artifacts they produced. Shiva was forever grateful for Indy returning Shiva Linga to the desolate village. God was grateful for him doing all he can to keep the Ark of the Covenant out of evil hands. Christ was grateful that he used the Holy Grail for purer means than what the Nazis and Walter had in mind. So during their annual All Myths Are True meeting in the afterlife, they watched over earth and noticed what was going on in Nuke Town. One of them said "Hey isn't that the guy that was protecting our stuff?" So they protected him from the blast. Why else was the fridge the only thing that was still intact, let alone with Indy safe inside.

The fridge was not an ordinary fridge
It was built as a special panic room from the artifacts from the secret warehouse and the nuke test would have tested it, but Indiana Joes just threw out the measuring instruments and went in himself. The FBI agents were mainly motivated by the Red Scare, but also a little bit at least from him messing with the experiment.