I have seen people produce what they called "differential"
ring oscillators which were in fact -not- differential, but
rather -complementary- (antiphase inverter pairs, the idea
being to make power currents not-steppy for other RF
reasons). Since your fill-form junk covers the circuit I can't
say whether this is or isn't the case.
Even a truly differential circuit has a finite PSRR and so
any supply (and ground) noise will have a finite influence.
But complementary inverters will be worse.
If your input threshold moves differently with VDD than
the average of the high and low output levels, or the
high-going, low-going slew rates, then this is a way
that supply noise can enter the signal chain. You can
get phase noise, you can get duty cycle asymmetry
/ phase overlap / phase gap, that kind of thing.