I am appalled to see that we, as a community here on Geekhack has not come closer to consensus to this issue.
So far I've seen two Filco keyboards that have the "Filco Ring". My other Filcos have had little or no pinging, or if they ping it's dampened right away. IMO there's a big difference between some slight or moderate "pinging" - and a loud, annoying resonance (of one note) in a keyboard's metal plate. This isn't a trivial issue, like a shine-mark on a spacebar. It isn't imaginary or FUD. "Sound samples or it didn't happen" isn't a valid criticism, because when samples are provided they're called fake. Anyway, I think it's hard to get a good recording of this.
Some other keyboards have a known problem with ringing. See for example
this review (linked to from the GH keyboard review section) of the Matias Tactile Pro 3, especially this part:
"Sadly, the Tactile Pro 3 does not achieve the same clean sound as other ALPS keyboards including the FILCO Zero range. My FILCO Zero XM has the crispest, driest sound of any mechanical keyboard, but the Tactile Pro 3 is quite the opposite: you’re treated to an excessive level of spring vibration from the switches, that gives it a constant high pitched ringing sound as you type. The switch mounting also gives the strokes a higher pitch sound, and the overall effect is somewhat disturbing. Spring reverberation is to be expected in mechanical keyboards, but it's absent from my Cherry MX blue FILCO and it’s absent from the ATK and FILCO Zero XM ALPS keyboards. I do hear it on my Cherry MX brown FILCO, but it’s not disturbingly loud as it is with the Tactile Pro 3. Placing the keyboard onto carpet does damp this excess vibration nicely though, so it’s probably a flaw in the way the switches are mounted."
I didn't try carpet, but I did put my ringing Filcos on a double layer of rubber shelf-liner and it didn't help one bit. I'm not a keyboard expert, but "it’s probably a flaw in the way the switches are mounted" sounds plausible to me. For the Filcos it isn't a general problem - it's just limited to some individual keyboards.