A “berthed”-friendly interpretation would be “all books start off tied to a particular point in time, it is their destiny to become free of their temporal bounds, to drift through eternity”
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.
If the arrow of time isn't berthing a book at its creation, when else would it?
The ambiguity is delightful.