The connection between the hamstrings and the sacroiliac joint is through what is known as the superficial back line myofascial meridian/anatomy train. If the hamstrings are tight, their tension pulling force will be exerted through the sacrotuberous ligament and onto the sacrum.
Muscles of the Lumbar Spine of the Trunk
Structural groups of muscles largely determine functional groups—that is, the structural location of a muscle largely determines its mover function.
Other Unusual Suspects
Semispinalis capitis, pectineus, & vastus lateralis are unusual suspect muscles, often overlooked by manual therapists, that can cause pain and dysfunction.