No one is disputing the possibility of ambiguity, but a few single-word examples is still a long way from "interpret any way you want." If you need to be precise about temperature or fashion or animal taxonomy or physiology, you can be, and a textbook is a better example than the observation that few people understand a language that is no longer in general use.
Notably, I wasn't talking about precisely-defined textbook words. If you go back, my original comment is directed at the fact that the Constitution can be liberally interpreted because the meanings of words change, which is due to cultural influence. Sure, we could go back and look at the history of America and figure out what "right" probably meant to the founding fathers (or "electricity" or yada yada for that matter), but to Joe Shmoe, the original meaning is either gone or no longer relevant. The only reason certain words' meanings don't change is because people aren't using them.
That said, I would still say natural language is, when you try to fully examine it without relation to reality, arbitrary (in a completely different argument), and while it doesn't mean "any which way we want" (initially), we could make a deep philosophical examination of the topic and come to that conclusion, but that's off topic. Though I feel like that's partly what you may have thought I was arguing initially.
We can only go by what you write, and you are making a more thoughtful point now. I do not think, however, that you can exclude "precisely defined textbook words" when the issue is whether natural language is necessarily imprecise (not that my textbook example is only about word definitions, FWIW.)