The problem with this argument is that it's begging the question. You're assuming that the Universe is behaving in a way that is consistent with how it appears.

There is no possible experiment you could in principle do to verify that the universe stays the same when you're not looking. We can say that the universe behaves consistently as though it does, and I'm not saying that doesn't matter, but it's not quite the same thing. Furthermore we can't tell whether the universe is tricking us some of the time, or all of the time, or never.