I think they call that trick the 'flutter.'

I don't know what specifically allows a tremolo system to do that, but not all of them are set up to allow it.

I have an Ibanez that does it really well; I just don't play it much. And surprisingly my Strat which doesn't even have a locking nut will also.

I'm like singtall in that I dismantled the tremolos from my guitars decades ago since I felt it had been overdone, and can be an easy crutch. However, I've heard things too that have me rethinking that.

My favorite example of musical tremolo playing is Alan Murphy's solo in Silent Running by Mike + the Mechanics.