Anyone that wants to "prove" that the RNG is flawed would have to test the RNG over a large number of crafts, gathers, other things, then parse the results properly before proceeding to analyze if the success rates match reality...

Having only done around 1000 gather sessions and counted number of HQ after that, I can only say that the HQ rate for gathers appear to be correct.

From crafts I've had HQ streaks at around 30% HQ rate and NQ streaks at around 70% HQ rate... Over a large number of crafts however, the listed HQ rates do appear to be correct there as well.