Technically, it is not a criterion, it is a definition. This is what is meant by proof, a, b, c, and d, and a is, the hypothesis must be able to be proved by a test that it can only pass if it is correct.
You want to use a different definition, fine. Please tell us what it is, though, before expecting those of us who want some a reason for believing something is true, to do so.
I think you also miss the point of falsifiability. All is says is, if you give something a test, any kind of test, and it can pass the test, whether it is right or wrong, the test doesn't test anything. It doesn't even say you have to give anything a test.
Hank