Looks like I may be mistaken about the rod. It's certainly the movement of the rod (moved by the diaphragm ) that "makes" the sound in a standard mic so I had presumed that an induction mic would be similar minus the diaphragm (so the air-borne sounds wouldn't get picked up) but I guess you are right that the coil itself picks up the magnetic fluctuation from the magnet in the speaker (hence the reason to get so close).
At least you have shown that the induction mic works correctly so we know we are dealing with either something to do with the speaker itself or, as you say, the low frequency causing a vibration in the mic which gets recorded if it's touching the speaker. Have you tried recording the same clip with the mic touching the housing and see if it's distorted at all?
Reproducing a problem will lead to the solution.
As a safety net, I'd buy a second mic though (not all of them are perfect so maybe you have one that's touching the plastic or something) as they are pretty cheap and, let's face it, most of us don't get to record in the parks that often so it's worth the expense .
I would think that outside vibration (within reason) shouldn't be a problem if the mic is OK (no moving parts).
At least, people pushing past me whilst I was holding one to the front of a speaker with one hand (bumping and sliding over the perforated grill) didn't alter the recording I did nor was there a problem (other than losing the sound) when the mic fell off a mushroom one and fell on the floor (no sticky dots with me)

Can others confirm that?
I know C33 took one to bits to see what was inside

Bear in mind I'm not well experienced in this form of recording (one holiday only) so take what I say with the proverbial "pinch of salt"
