a muscle cannot contract maximally if it is overactive (tight).
This is incorrect.
Reseach inidicates that stretching prior to a movement is counter productive to power output. Doing so inhibits the stretch reflex, mytatic reflex.
The stretch reflex is like rubber bands. As Einstein noted for every action, there is an opposite reaction.
This means when one does a slight bounce off the chest in a bench press, the stretch reflex provides more power when you drive up. The data shows up to 20% more power is evoked with this method.
Stretching prior to an exercise, dulls the strtech reflex. It like stretching the elastic out of a rubber band. The rubber band does not "spring back."
A better method is ballistic prior to a workout. This primes the stretch reflex to produce more power.
What may lead to increased rate of injury is neglecting a proper static stretching protocol before AND after training.
The research does not indicated that streching prior to a workout decreases injury. See the article Tim provided on stretching.
A static stretch after works best. Tendons and ligaments are like string cheeze. They are much more supple when heated.
One inteesting theory is that of John Parrillo. Parrillo believes in stretching (fascial stretching) after each set of an exercise. Hie view is that doing so allows for greater muscle grow.
I think there may be something to this.