Also, not racing-related specifically, but definitely automotive-related, this is a bit of "rumor-paranoia" that gets told incorrectly quite frequently.
In' 60, Chrysler Corp. president William Newberg, who had just received the position in that year, overheard Chevy general manager Ed Cole talking about a new "smaller" Chevy at a Detroit garden party. Shortly before this Chevy had launched the compact Corvair, so Newberg assumed that GM was going to downsize their fullsize cars in response to growing Rambler compact car popularity and the recession of a few years earlier.
Newberg went back to the office and immediately ordered Virgil Exner to do a crash-course redesign of the upcoming '62 Chryslers. Exner had been struggling to top his '57 designs to begin with and then was forced to take the fullsize cars and squeeze the styling down onto a stretched Dart/Valiant chassis. Also, accountants took charge of the program, demanding that the redesign be done as cheap as possible, meaning they couldn't use planned wraparound bumpers, curved glass or the new roofline Exner had planned. Exner protested loudly at every step of the way, but was overridden by Newberg who did not want to be caught out by GM's "new smaller car". Also, although the rumors would have been quite easy to double-check, due to Detroit being quite an insular place at the time, nobody eve did or questioned Newberg. Instead, they deluded themselves that the downsized '62s would be a big hit.
Before they hit market, Chrysler did an internal audit over accusations that executives were handing out contracts to companies that they had financial interests in. Low and behold, Newberg had interests in 3 Chrysler suppliers and had received about $455,000 from them. Stockholders thew a fit and Newbeg got outed after just 60 days. Lynn Townsend took over from him.
By this point the restyled '62s hit the market and torpedoed, with a 25% drop in sales. The styling was absolutely bizarre and awkwardly jammed on truncated chassis. For years dealers had been telling people that bigger was better and then Chrysler did the exact opposite. And despite being smaller, they still cost as much as the competition. Chrysler needed a scapegoat, and with Newberg gone, they fired Exner due to the cars being his design, despite the fact that he was the only one who protested the idea. Even more irony, Exner's 63 designs sold massively well.
And the "new smaller Chevy": It wasn't a downsizing of fullsizes. Ed Cole was talking about the upcoming Chevy II Nova.