There is another chance, though.
has happened to me several times.
designed FM tube amplifier can have a cavity of a very high Q.
sometimes a not
so well trained engineer can mistune such an amplifier to have the output varied in
amplitude as the frequency of the modulated carrier slips on the slope of the Q curve.
If the amplifier is powerful enough , the output power variations can be such that
an AM modulation depth of several watts (even 100 watts @ kw) is observed (I have seen
it with my own eyes (!) fwd meter dancing along with the beat.)
since it is already
biased and self-slope discriminated, such a signal doesn't need detection, a capacitor
is more than enough to filter rf and to provide crystal clear audio!