The CIA leaked that Bishop had been killed 14 months earlier in the CNN report following the Muir leak. The Agency could no longer claim he was rogue to the Chinese because they extracted them both. As such, they would have buried it from the press and retired Bishop out under NDA. The Chinese would have been handled diplomatically with concessions easily because the Chinese would not have wanted any word of the breakout having occurred. Especially at that time it was all about saving face and trade.
My brother was in operations for 12 years there until '93. He says that there is a huge divide between ops and the suits in admin & analysis. He said the movie was a stretch but was certainly told from an ops POV.

Oh for sure! Either way, they were going to end up better than they would have in a Chinese Prison but that's not saying much. I agree with the OP. As a happy ending goes, it's kind of a wet firecracker.

assume they are both pretty screwed. Well that sucks!
At least they're alive, which is about all Muir can realistically do for them.

Okay since I've seen this movie like 50 times
I feel really dumb about never thinking about that. You're right, without something telling us they some how ended up in some non-extradition treaty country, we have to follow the logic of the movie and assume they are both pretty screwed. Well that sucks!