The performamce of most active regulators will start to degrade above a mere 1KHz.
At that frequency, it probably will be the ESR of the capacitor used at its output...
how much is the output impedance of the LM317 at 1Mhz? is it 0.11ohm as I read somewhere.
It might be better to say 1.1uH instead of 7R.
It is not Z rising with frequency which makes it inductive, but Z at a perpendicular angle.
Resonance with C is inconsistent with the resistive impedance which Elvee measured. Perhaps he could give more details of his measurement?
A zener boosted by a follower would not show rising impedance with frequency, unless the follower was quite a slow device. Maybe it is a slow device?