I have several simple setups where I only use a capacitor on the regulator output and they work ok (well, for 6+ years).
No you haven't you have several simple setups where you have not detected the instability.
The last data sheet I read on the regulator chips only recommended the caps on the input side when the input was over a long wire.
That was one manufacturers claim on one specific chip, did you use that chip 6 years ago?
As to stability, it is a relative term
No it's quite specific.
as to the actual operating conditions and requirements.
Hey lets redefine words, I can balance an egg on it's point, that is stable as long as nothing disturbs it.