The connotation of "assigned" has always been for me that it is largely at the discretion of the assigner. If you're assigned custody, it could have been otherwise just on the say-so of the authority. If I'm assigned as the designated driver, it could have been otherwise save for the social decision. If they are assigned clean-up duty, it could have been otherwise save for our decision that it was going to be them.

Why "assigned" rather than "observed" or "determined" or "presents physically as" or simply no word at all? Why not "notated" or "witnessed as"?

Why assigned? There are so many words to choose from--why pick the one with such connotations unless you want to suggest an arbitrariness to it?

And in fact it is arbitrary in (quite rare) ambiguous cases or unusual development, and we haven't historically handled those particularly well. But the connotation is far stronger than the reality of the situation, which is that the determination is made based on physical morphology which is characteristic in almost all cases.

Maybe the connotations aren't particularly obvious to you, but they are to me.

Also, I'm advocating that everyone take everyone else at their word unless there is compelling evidence that one shouldn't. Sometimes there is good evidence--people are not infrequently duplicitous--but it's worth making the case if you want to convince anyone save those who have already decided the same on their own.