Two words: artistic license. From what's been written, about as close as the whole NF-104 Starfighter sequence came to the actual event was, "Chuck Yeager flew the NF-104. It crashed. He survived". The filmmakers wanted to continue the whole Yeager-Ridley relationship to the end because it made for a better film.
Consider if Ridley hadn't been there, who would they have used? The audience would have been like, "Who the hell's that guy? Where's Ridley?". Or if they'd stuck to the facts, there wouldn't have been any of that 'good ole boy' crap, at all. Yeager would have filed a flight plan, the controllers would have known about it, and someone else would have been on the emergency crew to pick Yeager up after the crash, anyway.
So, yeah, Ridley being there for the NF-104 was a big stretch, but the bottom line is it just made it a better movie.
The real irony of Ridley's fictitious presence at the NF-104 flight is that if he actually had been there, Yeager might not have crashed. It's been suggested that Ridley was a big factor in instructing someone like Yeager (who lacked the same, extensive, formal education) in flight dynamics at the speeds and altitudes they were flying back then. When Ridley was killed, Yeager lost a crucial flight aid.
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