You're assigning some notion that berthed means berthed in a home port. Ships are berthed in many different places and times. So the "time which berthed them" just doesn't work.
Mixing metaphors and claiming a now-unmoored vessel is more likely to be contrasted with one in a state of being “born” than “berthed” is what “doesn’t work”.
Especially considering “unmoored” is a nearly exact antonym of “berthed”, whereas a ship is never described as being “born”. Christened, perhaps. But certainly not born.
Perhaps you're right and it was remembered or quoted wrong, and the word really is "berthed", but it wouldn't have been just the one word remembered incorrectly.