UP is about trying to understand the reasons behind the child's behaviour and trying to be respectful of that but you as the parent are still responsible for managing your child's behaviour and raising them responsibly. It's not opting out.
For instance, in the bath example, it's about trying to figure out why the child doesn't want a bath - is it something physical, like the water being too cold, or something emotional at the root like the bath seeming claustrophobic from inside or perhaps the child doesn't want a bath as he/she was enjoying 1:1 parental time before and doesn't like sharing the bath (and parental attention) with a sibling... and then you do what you can to fix the issue. Sometimes the issue can't be fixed and it is a non-negotiable but if those instances are minimised then generally the child is less resistant.
DD's 2, there are plenty of times I could get DD to do what I want just because I am bigger than her but the times when I have to do that are quite rare. Having said that, Kohn's book is about an approach rather than a practical how-to, and it is challenging to get away from rewards and punishment behaviourist model of thinking, mainly I think because that's how I was raised, and I'm not above chocolate button bribery on occasion...
It annoys me that UP gets such a bashing by people that don't really know what it is - if you can't be bothered to read the book, or at the very least google the term and do a bit of the background reading on the UP website, then how can you actually debate it's merits and failings from anything like an informd position? I don't knock people who choose to use star charts, it's none of my business. I prefer this model, it seems to work better for me and my child. It's not that long since people who didn't smack their children were thought to be weirdly permissive.