Assuming that yours is a 'component' FM tuner (du some old jour) and it has the usual layout of stages ... (Not a plastic cased Granco model with no RF-amp)
IF the AGC [automatic gain control] feedback loop on first RF-amp stage has suffered a well-drifted carbon resistor or leaky small cap/amidst its components:
could be that "it is no longer a real AGC", but is very unhappy with more than say, a few hundred µV input so it simply clamps to zero. Your air-gap evades the issue by not addressing it: happenstance maybe supplying just the right level for the IF to do its frequency magic and get a decent signal to the discriminator (or ratio-detector) where Mr. Armstrong's bitchin idea converts it to decent audio.
[Also if your antenna has a preamp--an added stage to vet by substitution: initially just a straight wire, right?] That you suggest: it may be better than (you recall, ever?) would imply that the tuner had a bad RF stage for donkeys' years.. Fisher 100, 200? H. H. Scott [??]
Anyway if you decide to sleuth it to a fare thee well, I have here a Sound Technology 1000A Broadcast-grade alignment generator (of vanishing-small distortion, IM or Harmonic)--an actual complete broadcast-grade source, as in--add a power amp and antenna: you're on the Air Indistinguishable from the Official (also legal) others. Lots of lesser-quality units are out there in small towns ... rarely challenged less'n they pick a frequency that drowns a distant station the locals like.
(I need to find a tech who still likes perfectionist repairing..) When I was dabbling in that, I couldn't/well.. wouldn't afford this state/art gadget ..and then Muricans drifted away from larnin stuff and into MBAs, and well, you know. Might even be worth the RT shipping, should you get a perfectionist heat-on.. knowing exactly what you are transmitting makes such a weirdness as you describe: almost a pleasure to screw with!
Else, carrion. If you can bear to never get to.. the bottom of this magical phenom. ;^>