A client I began with last week had this exact problem. He had been to a physical therapist for a couple of years who misdiagnosed the problem and he himself also "felt" that his hamstrings were stiff. However, when I checked the other joints around his hips and simply looked at him stand, it was easy to see that this couldn't be farther from the real issue at hand. He had an anteriorly tilted pelvis.
I should point out that an anteriorly tilted pelvis also increases the curve in the lower back, which overstresses this region also and often causes back issues. Guess what, stretching those hamstrings makes the issues worse.
So what do you need to do to fix the problem? First of all, stop stretching your hamstrings, which are already on stretch. What you need to do is stretch your hip flexors (primarily rectus femoris, psoas, tfl) or for the simple minded the front of your hips, and activate/strengthen your glutes. Doing this will tilt your pelvis back in the direction of neutral, take the stress off of your hamstrings and back, and make you feel like a million bucks again. The hip flexor stretch, glute activation work and soft tissue work that I covered in previous posts are great ways to begin doing this.
Before I go, you should note that this is not the case with everybody. Some people really do have stiff hamstrings that need some length. Everything must be checked to determine what is really going on. Assumptions will get you nowhere. Hope everyone has an awesome rest of the weekend!