Yep, should be no continuity to ground.
If you really wanted more details, you could take an ohm-reading to ground on each leg, not just continuity. This would tell you which of the 3 phases went to ground.
That all being said, 13.5 volts at 3k is liveable... It'd keep the battery charged anyway. But, you'd want to limp HOME from vacation that way, not start OUT on vacation that way.
Good luck with it all.
Kirk