The discussion of Bud Powell starts about 43:00.
At 47:00 of so there's an explicit discussion of influence and competition. He's right, cutting contests are part of the jazz tradition. But that kind of highly ritualized bandstand combat is one thing, influence is another. Bloom seems to be conflating the two in his remarks. I've read many anecdotes about jazz musicians listening to records or broadcast performance and being inspired what they hear. That's influence. That runs orthogonal to real-time competition in cutting contests, which musicians will mirror or complement one another's lines. Whether or not that activity has a permanent influence on a musician's style, that's incidental to the real-time musical combat.