Not exactly: they oscillate because of impedance transformation resulting in a negative input impedance, which can then sustain oscillations even with a lossy (but reactive) input network.Isn't the reason that emitter followers can oscillate, that their Zout becomes inductive with higher frequencies?
This reactive part can be provided by parasitics, especially in high Ft devices
Dennis Feucht has the most comprehensive analysis I've seen anywhere - http://audioworkshop.org/downloads/AMPLIFIERS_OSCILLATION_BJT_CIRCUITS.pdf
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