I could be completely wrong, but I would imagine that exercise, though it breaks down our protein, likely stimulates some mechanism that would then enhance our bodies' ability to digest, absorb, and process protein. If there's a post workout window for carbs, I figure there's probably a post workout window for protein too, and maybe it lasts much longer than the carb window? Just a guess.
In any case, I know when I eat truly keto, my urine smells like ammonia, so I'm not surprised that not eating carbs increases nitrogen excretion. You're probably eating even more protein than you normally would as well.