Iron Man was also recorded in the UK at Air Lyndhurst, with UK session musicians. The only Marvel Studios film that utilized U.S. musicians was The Incredible Hulk using the Northwest Sinfonia, but even that was non-union.
As for The Avengers and Captain America, Silvestri definitely used most of the same musicians from the LSO to record the score. But some of them were contracted from other orchestras, like the London Philharmonic, Pro Arte, and Royal Philharmonic. That's why it's not credited as the LSO.