I don't see a problem with the LLM answer. The field near an FM station can reach 100mV or more. The maximum safe exposure levels for general public at 100MHz is 30V/m according to standards.
It's easy to lose a sense of scale in a field which usually works in logarithmic scales. Signals can easily vary by more than 40dB, and it's easy to forget that's a factor of 100 already, and another 40-60dB is not crazy in edge cases. (OTOH ~100uV is a much better estimate of what you'll be seeing from a 'good' FM radio signal)
The part about FM sounds like BS, but much more than 1V at the antenna is definitely possible if you're close to an AM station, enough to cause unintentional receivers to emit sounds.
Well, I'm expecting an average case, not "playing AM radio with grass", because in the vast majority of the cases, antennas won't be situated within a few meters of the radio tower:
Making total power for the 30cm shell = 0.44 picowatts.