Trouble is, there is lots of hyperbole but little hard evidence for what happens in concert or rehearsal settings, to say nothing of who was in the audience. Recording and release dates at least establish some basic chronological benchmarks.
That said, your argument serves to reinforce my point. Chico, like other jazz artists, was likely performing the music and arrangements heard on those albums months prior to the recording sessions. The rock and pop groups of this era, by contrast, were generally working things out in the studio just prior to the sessions. They were often playing Chuck Berry and Little Richard live while they were adapting the Tibetan Book of the Dead for lyrics in the studio.
So, if anything, Chico would have been a greater influence on the aforementioned groups than the other way around, at least in terms of the eastern influence.