Yes it does seem backwards. However, nobody here is making that argument.
> I'm over here trying to find a minimum amount of government authority over our bodies
Perhaps I'm just splitting hairs at this point, but "No one, not even the government, should have more authority over your body than you." is just such a broad brush that it's trivially refuted for certain scenarios. Maybe you're talking about medical authority?
In any case the rule of law is very concerned with what happens when rights collide. It is possible -- perhaps common -- for individual's rights to be in conflict.
Maybe. It has much less rhetorical flourish though ;) I still think it's a valid ideal and even if realistically unobtainable in the absolute, it still incredibly worthwhile north star.