the hamstrings attach to the bottom of the pelvis, your bum bones. If they are tight, the muscles pull on the pelvis where it attached---> posterior pelvic tilt. If the pelvis is already tilted at rest, then the lumbar spine naturally will slightly flex. Though could present as a 'flat back' with less lordosis. It can lead to strain on ligaments and structures and definately gives incorrect movements patterns..

Many people work on hams length if they are tight in those with lower back pain, and it does work. but there is not a set outcome in a number of studies though, some say that they have not had conclusive evidence. but my clinical experience has always found that it does affect the lower back.

this study ingentaconnect Effect of stretch positions on hamstring muscle length, lumbar fl... compared stretching hamstring for 4 weeks and found that it did not affect lumbar range of movement. but then they were not looking at pain levels.