Well, guys, problem solved ! Guess who was right ??????????
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JAZZZZZZZZZZ !!!!!

The 5V signal to the BOB had two routes to 0V... getting the 5V from the PC solves the problem :) This is why disconnecting the PP cable was causing the noise to go away, since it would suppress one of the two 0V possible routes.

Thanks for your help !

I do have one more tiny issue:
Mach3 controls the RUN/STOP signal and spindle speed fine, but the BOB seems to output an unstable signal for the spindle speed control. When running, the frequency can't stay still and keeps going up and down by 1-2 Hz, causing the spindle to run faster/slower (you can hear a slight increase/decrease in speed).

I can bypass this issue by disabling Mach3 speed control and only do the RUN/STOP, but while I'm at it, let's fix this issue if possible :)