Can stretching prevent pulled hamstrings?

Typically when an individual pulls their hamstring they immediately zero in on the hamstrings and begin to look at increasing the flexibility. Unfortunately that is looking at the body in an isolated fashion. The body is a complex integrated machine that when all parts are working good the potential for high performance can occur, on the flip side when the parts are not all working there can be an increase of injury. The site of the injury is very rarely the cause, the cause is usually elsewhere and generally there is more than one cause. Begin to ask yourself why did the hamstring pull in a specific task. For example, if it was pulled while running begin to look at the feet. The foot is the first thing that strikes the ground in running. If the foot is not loading and moving properly this will cause the tibia, femur and hips to move less efficiently. Moving less efficient can cause compensatory patterns through all the muscles around those landmark bones. Instead of the gluteus musculature firing properly for example, the hamstrings would have to work harder and be more susceptible to being overworked and lead to potential injury. 
 

Stretching prior to exercise will definitely help to prevent a pulled muscle. When we exercise are activating and tightening our muscles as they work through the exercise you are completing. If you do not have some form of a stretch prior to exercise then those muscle may not be properly conditioning for the exercises you are about to complete. All of this may result in a pulled hamstring and that would not be something fun to experience.

Stretching can help prevent pulled hamstrings.  I recommend stretching in an dynamic fashion (active isolated stretching) or using the foam roll.
Tight hamstrings can be a result of tightness in other areas, so make sure to stretch your lower body through the mid-back to attach the issue in comprehensive fashion.

Increasing flexibility of the hamstring muscle group can greatly reduce the chances of pulling either of those muscles but there is always the possibility of pulling a hamstring. As Dr. Roizen stated, "The hamstring, a group of muscles that support the hip joint and attach to the lower leg, gets injured from overuse, especially if you're over striding during a run."
With this being the case, engaging in a proper active warm-up will be beneficial to you prior to activity. The one thing that you do not want to do is stretch a cold muscle, as it is more susceptible to injury in a cold state (by cold I mean not warmed up or any pre activity). After a good active warm-up (5-10 minutes), additional static stretching will help the cause.