So I recently desoldered (for the first time!) all the switches on my broken Filco MJ with Cherry MX browns which is about 3 years old, and when testing some of the switches I noticed some of them had a really bad ping when I depressed the switch then let it snap back, and the sound was more or less very similar to the Filco ping thing I've experienced and gotten used to.
So, to sate my curiosity, I did a couple of experiments. I took apart a pinging switch, and switched its spring with a switch that didn't ping the same way. What I noticed was that this fixed the ping on the pinging switch but did not introduce a ping on the new switch.
Next, I reseated the spring inside a pinging switch, to test the premise that it wasn't the spring or the switch, but something to do with either the placement of the spring or switch housing itself that was responsible. This also fixed the ping! I repeated this with a few other pinging switches and it worked with all. This seems to suggest whatever I did reduced the resonance within the switch housing enough to eliminate the ping.
I'm not sure why I got the results I did, but maybe you guys will be able to try this for yourselves - after all, you are keyboard scientists and I am merely a clueless nub