Proper muscle balance is key to staying pain-free. If you have tight hamstrings (which do attatch to the pelvis), it does have the potential to cause poor posture. If it causes your low back to round out, you will have extra stress on your low back. However, any muscle imbalance will eventually cause issues. Sitting for extended periods of time (like at a computer or horseback riding) will cause hip flexors to become tight. This, in turn, leaves the glutes underactivated. Hamstrings usually assist in hip flexion, but if the glutes are in need of help, the hamstrings and muscles of the low back will have to kick into overtime to help out those glutes. All this compensation leads to pain and possible injury down the line, over time.
So yes, the hamstrings can cause pain, but don't be afraid to have a professional look into the cause. Oftentimes there is a reason why they are working too hard or are found to be tight. A whole-body approach might be necessary.