I should elaborate, I suppose.
Two things can happen when one uses a tremolo system. One is that the string is "overtensioned" or tension is reduced, thereby changing the pitch. The other is that strings whose tension is altered can change their position; wound strings in particular, since the windings can catch on the nut. In the case of Bigsby-types, the traditional recommendation is to use roller bridges, since the saddles are stationary and the strings are pulled back and forth. The risk is that wound strings, and even unwound, can catch on the top of the saddle. Rolling saddles are intended to avoid that. Locking tuners are also used to attempt to compensate for what tremolo systems might do to string movement when tensioned or untensioned.
In addition to bridge saddles that "forgive" changes to string tension, people will use nuts made of different self-lubricating material, or apply things like "Nut Sauce" to saddle grooves to provide lubrication and prevent strings catching. That is often associated with strong encouragement to use "well-cut" nuts. Seemingly contrary, but really part of the same overall don't-let-them-move-the-wrong-way strategy, are locking nuts, the idea being that if the string is locked down at the nut then it can't move and catch on anything. Fixing the string at both ends, by effectively screwing it into place would seem to make tremolo purely a function of tension alone, and factor out any string movement. Personally, I find locking nuts a bit of a nuisance, no matter how much the physics would suggest otherwise. One still can fine-tune strings at the bridge with the adjustment screws, but I'm more inclined to tuning keys myself. That's a matter of personal preference, rather than any sort of "physics-dictates-you-must"argument.
