Your grounds are fine. You can tell because the noise goes away when you touch metal on the guitar, so it is clearly connected to ground; the same thing will happen if you just hold the guitar and touch any other grounded metal - like say on the amp, or via a wire to the ground lug on an outlet- because YOU are being grounded.
The guitar, and your body, act like big antennas picking up all the RF noise in the air. When you just hold the guitar, your RF noise gets radiated into the electronics/pickups. But when you are grounded and hold the guitar, you act as a big shield for the guitar and all the noise you collect is dumped to ground instead.