Two airlines I worked at previously required a rerelease if the aircraft had moved under its own power. I know that's not the case at Delta but it seems very strange that the FAA would approve both of those FOMs (one of which was written by NWA people and patterned after the NWA FOM) if that proviso was contrary to the regulations.

OTOH, sailing is 100% correct that many of the provisions of the FOM have the full force of regulations. For example, there is no FAR 91 or 121 requirement to fly a stabilized approach, it's a FOM requirement...but I have no doubt that if I continued an unstabilized approach to landing with a fed in the jumpseat, I'd get a violation.