Yes, your basically correct. The faster the twist, the heavier the bullet it will stabilize.
Bullets spinning too fast is only part of the equation when a bullet desintigrates. It usually only happens with lightly constructed jacketed varmint bullets, fired at high velocities from rifles with "sharp" rifling.
I experienced it with my then new 788 Rem in 22-250 when shooting Sierra BLITZ bullet handloads. It didn't happen every shot, but a couple times I shot and the bullet never made it to the target. Then with the second shot you would see only one bullet hole in near the bull.
CW