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.
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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