I've heard the same thing... that certain species of pyram snails eat certain things... but can cross over if forced to... I've read stories of them killing a clam then moving on to snails afterwards...
If you've got pyram snails on your snails... they may be incredibly difficult to eradicate, and yes, they will multiply into sufficient numbers to kill your snails.
I'd suggest quarantining your snails as you find them. Pull out every snail you can see, then keep pulling them as more and more come out into the open, and scrub the snails off the ones in quarantine on a regular basis with a toothbrush. You'll probably lose some snails, because as you pull snails from the DT, the pyrams will concentrate on the few that are remaining and overtake them. Once you stop seeing snails in the DT, leave them out for a while. Pyrams are obligate feeders, and once you get rid of their food supply, they'll die off on their own, and you can re-introduce the quarantined snails.