For a simple double-pole loop response, when the phase margin drops below 45 degress then the amplifier tends to ring when settling. The larger the gain, the longer the ringing. At 60 degrees phase margin, you get optimal settling time with no ringing.
So although your system needs 0 degrees phase margin to oscillate, you can get ringing that is so long that it's virtually oscilalting with small phase margins and large gains. Secondly, once the ringing reaches large enough amplitudes that it starts to saturate the amplifier, the non-linear effect will cause frequency shifting and create a permanent oscillation.
Greg