It's an interesting point about updating movement automatically to avoid a bullet. I did consider this possibility before, however I assumed that this would not give you full invincibility because if you are standing in an area and bullets are being fired all around you it may not be possible to move to a position where there is not an incoming bullet in time. Although even with this you could still gain a significant advantage.

Also a lot of older games would mainly use a hitscan model for bullet collision detection. The projectile itself was not modelled, instead there was a ray intersection test done at the time the bullet was fired so there was no "movement" for the bullet so to speak. Do most modern games now use a physics engine to simulate every bullet instead?