Actually, I heard another, not nearly as favorable account of the NF-104 incident from an engineer on the program. It's hard to say where the truth lies as Yeager has a - let's say - disagreeable personality and makes lots of enemies.
According to this guy, Yeager actually lost control of the aircraft twice. It was known that the F-104 had an unrecoverable spin mode with the engine out (apparently, the motor was big enough to generate a stabilizing gyroscopic force) and since the a flameout was a high probability, the NF-104s were fitted with spin chutes. So after the initial departure from controlled flight, he deployed the chute and recovered the aircraft. Instead of descending with the chute deployed until he reached the re-light envelope as they briefed, he decided to cut the chute to get down faster. But without hydraulics, the flight controls were still configured in the position that caused the initial spin and he immediately entered the second one which he had to bail out from.
Between the unauthorized record attempt (he didn't quite steal the airplane like in "The Right Stuff," but it's close) and the failure to follow procedure for the spin recovery / relight, it would have been end of career for any other pilot. But I guess being a national hero buys you a few "get out of jail" cards.