Perhaps this illusion is the result of an acoustic rather than physiological or cognitive phenomena.
Record a sound from a musical instrument - something with a well defined harmonic signature - and edit the recording to remove the fundamental.
Play the recording through a speaker, in an ordinary room (not an anechoic chamber) and re-record it and examine the recording.
Does the fundamental re-appear (at reduced amplitude) in the new recording?
Has anyone tried this?