[tyingq]

It's an action though, "the time that XXX'ed them". Birthed fits there well, berthed does not. Had it said "the time they were berthed to" I would understand your point better.

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.

[basil-rash]

There is no categorical semantic difference between "berthed" and "birthed". They are both past participle tense verbs and fit equally well with no changes needed to the rest of the sentence. Perhaps you simply have more experience hearing birthed in that context and perceive it to fit better? But in reality they really are grammatically identical.