I'd be interested to find out if anyone else is able to reproduce this

I have had this same problem. I have a noise S&T board in my Fireball II. After installing a cap kit in the board, it was still noise and when I touched C24 or C25 I got a local A.M. Spanish station. I thought it was pretty funny. Still have the noise problem too. I have moved the board away from ground, gave it a better ground, replaced and socketed the PIA's and Rom's, replaced the amp, replaced speaker, replaced trim pots. This board has me stumped for now, I will come back to it later. Board does everything it is supposed to do but is still noise. I know that the problem is on the board to, I put a friends Fireball II board in and it was quiet.

I had this happen with an Elektra when I touched the board while it was on.

Just how does the pinball electronics pick up the analog radio signal?

The wires act as an antenna, and the cards amplifier circuitry amplifies it to audible levels.

Sounds like Gilligan's teeth....

I had figured out the antenna, amplifier and speaker parts of the equation. The other parts needed like the basic tuner wire or resonator. Also the detector diode (germanium diode). Is what escaped my understanding, how it would pick up a signal.

Quite common by just touching a volume control pot (metal shaft versions) or touching most parts of the sound board on pins that were on location in the downriver Detroit area. WJR's transmitter is located there and it's a 50,000 watt clear channel station.

The great voice of the Great Lakes. RIP JP McCarthy.

Had a similar issue with feedback in the speaker, changed everything (or so I thought) ended up being the contacts for the speaker. changed the ones in the plug with new .156 crimps and feedback went away. easy way to check is wiggle the speaker connector when you hear the noise if it goes away thats your prob.

Haven't you ever read the FCC disclosure on the backbox?

Ummm ya.. a quick glance or two. That FCC disclosure was there because a pinball machine creates an interference of some kind.

and also must accept any interference the may cause undesirable operation.

You forgot the envelope detector. Any diodes that happen to be in circuit with the received rf signal are acting as a half wave rectifier, revealing the audible sound peaks and valleys riding on the passband carrier wave. Also, filter caps may remove what's left of the residual passband signal.

The input circuit just happens to be naturally tuned to an active AM radio station frequency, possibly more than one if it has large enough signal bandwidth or multiple resonances. The fact that speaker wire is typically at least a foot or two long is probably acting as a quarter wave whip antenna since AM frequency wavelengths are extremely wide.

It goes without saying this is a very interesting phenomenon. I've heard the same thing when setting up an arcade machine in a bar. Can anyone get some video of this if it's happened with their games?

Here in the USA, ASCAP & BMI would probably try to sue a route operator if they found out about this.