This is a strange statement. Many pickup designs have springs as part of their mounting mechanism, but it's not for dampening vibrations - it's to allow the height of the pickup to be adjusted.
Certain pickups (notably, off the top of my head, Fender Jazzmaster & Jaguar pickups) don't even use springs for this - instead there's a block of foam placed underneath the pickup that compresses as the pickup is screwed down.
Of course, it's possible some cork-sniffer guitar nerds will claim that they can hear the effects pickup springs have on tone (and the effects of different metals in the springs, no doubt), but these are the same people who will claim that they can hear the difference different glues make on tone, or will swear up-and-down that a real $5000 Klon has a richer and fuller sound than a $100 clone made from the exact same circuit with the exact same components, or that tube amps sound better because "electrons can't survive in a crystal lattice" [0] (so buy my $100K tube amp!), or...