I'm not aware of that story, but there is much speculation about why Yeager was never selected for the astronaut corps. His biography (I haven't read it yet, it's second-to-next on my shelf) specifically mentions that Chuck "had the right stuff" which during the Mercury time was code word for "good enough to be an astronaut".

I thought it was explicitly just that he didn't have a college degree? Or is there more to it than that?

In his own words:

JC: Any regrets you were never selected by NASA as an astronaut?

CY: In order to get into the space program, you had to have a degree. I only had a high school education. In the early Mercury program, everything was done from the Cape [Kennedy] anyway. The guys didn’t have a hell of a lot of control, and that to me isn’t flying. I wasn’t interested.

https://www.forbes.com/sites/jimclash/2017/01/23/chuck-yeage...

I'll know as soon as I finish the book!

> Q: Why didn't NASA ever select you to become an astronaut? A: They knew I didn't want to wipe the monkey crap off the seat before I sat down

Edit: https://twitter.com/genchuckyeager/status/918320874947715074...

The X15 was built by North American, and I do not think Yeager flew it. You may be thinking of an ill-conceived idea for Yeager to use one of the NF-104A rocket-boosted Starfighters to set an altitude record. According to this series of articles by the pilot running the NF-104A test program [1], Yeager did not follow the flight profile and consequently ended up in an irrecoverable flat spin from which he had to eject. Yeager could not be blamed, so the author claims he got shafted by the inquiry, with no opportunity to defend himself.

[1] http://www.kalimera.org/nf104/stories/stories_11.html http://www.kalimera.org/nf104/stories/stories_12.html http://www.kalimera.org/nf104/stories/stories_13.html