This is all well and good in theory, but the number of times I've seen tests that don't actually test what they say they're testing is hard to count. Yes even when you encourage the developers to ensure the test fails first and do TDD. Tests help you ship with confidence but there's usually at least a few that are just passing by pure luck.

So no, I wouldn't judge a rewrite as being equal just because it passes the tests. That said, I don't think that means you shouldn't do it. You just have to be pragmatic about it.