Interesting theory. To throw out some 'anecdata' (maybe we can turn this into a sort of study?) - my three-device test (iPhone 6S and Pixel 2 XL at 60Hz, 12.9" iPad Pro at 120Hz) would seem to indicate that the refresh speed does not affect the touch refresh rate, however, this could be the result of the large performance differences between devices used, as the average and maximum times trend down with the newer/faster devices in testing.

Min/avg/max of 10 taps, as fast as possible;

    17/26.6/36 -- iPhone 6S
    16/23.7/34 -- Pixel 2 XL
    17/21.7/33 -- 12.9" iPad Pro

I would probably conclude overall that my hands are just slower than yours!