One other thing to think about that I should have been more clear on --
If your hamstrings are "stiff as a board" that inclines me to think they are that stiff because they are picking up slack for other muscles (most likely your glutes and abdominals).
I already mentioned something similar on a recent thread so I don't want to beat the subject to death but the best way to think about your body is cause & effect - it tends to produce a kinetic chain of events. It's hardly EVER 1 issue. Your hamstrings are most likely not tight simply for the sake of being tight and will respond cooperatively to some simple stiff-legged stretching at the bottom of your driveway before/after a run.
To be more specific - think about what your hamstrings do. They are a major hip/thigh extensor. What other muscles are major extensors? Your glutes are, especially when running. If these are not working at an optimum level (maybe because you sat on them 1/2-3/4's of the day) then who do you think the next muscle will be to take over their slack? Your hammies. Chances are if you have inhibited glutes you also have inhibited abdominals.
"But I have a six pack!!!"
Sure you do. So does every guy I see at the gym who comes in whining about their tight hamstrings, dynamic disc bulge, and flexibility problems. They can do 1,000 crunches no problem with 120 lbs of cabled weight. However, if I ask them to lay supine and tilt their pelvis into a neutral position by bracing their abdominals and then to hold their legs 6'' off the floor without allowing their pelvis to tilt for a mere 30 seconds, they are half pissing themselves by 25 seconds and I can see their pelvis tilting slowly but surely even while their abs are busting through their t-shirt.
I'm not saying you have ALL of these issues (although it's not unlikely at all). But my point is if you want to maximize your performance and reduce injuries then truly address the issue.