people claiming he actually was a top mathematician in every sense of the word
He did score top 5 in the Putnam in 1939. Whose competitors would be all undergraduates in the U.S. and Canada. It was only the second year the competition was offered, and I don’t know what fraction of top math students actually took it, nor how much Feynman prepared for it relative to his competitors; nor is math contest skill identical to math skill. But, all that said, if we count his contemporaries as those within ±10 years of his age, then this would appear to put him in the top 100 on whatever it was that the Putnam tested.
Edit: There is also a claim that Feynman said, in an interview, that someone who graded the 1939 Putnam (Feynman didn’t name the competition, but it fits the description) told Feynman “Not only were you one of the five [winners], but the gap between you and the other four was sensational.”