The people you mentioned are probably insured for structural or mechanical systems defects. They will probably not honor a cosmetic claim so you would have to prove the foundation in indeed faulty and not normal movement.
I would define faulty as part of it moving and going to continue to move, in one direction, until the support or framing fails. It doesn't have to settle much to cause stress cracks at corners and joints. You may find, like I did, some of the cracks open and close seasonally.
That said, if part of the foundation is going south and continues to do so, you have a claim. In that case you might well let your homeowners insurance company lawyers go after them, if you can.
