That may be the best we can do, but it would have required sub-arc-second accuracy to measure the parallax to the nearest stars, and the science of astronomy was nowhere near that capability in Galileo's day. Thus, the superiority of the heliocentric view was unprovable, since it was indistinguishable from the geocentric view.
It's more of a philosophical position than a scientific one.
As for the parallax, the extent that's been measured was in the range of 0.00000x degrees of a shift.
That may be the best we can do, but it would have required sub-arc-second accuracy to measure the parallax to the nearest stars, and the science of astronomy was nowhere near that capability in Galileo's day. Thus, the superiority of the heliocentric view was unprovable, since it was indistinguishable from the geocentric view.