nUnit Assert.That(method,Throws.Exception) not catching exceptions
Try this instead:
Assert.That(() => Int32.Parse("abc"), Throws.Exception.TypeOf<FormatException>());
Basically you need to pass a delegate to Assert.That, just like the documentation in your link states (note that I've used a lambda expression here, but it should be the same).
What test runner are you using? Not all of them work correctly with the exception assertions.
You may have better luck using [ExpectedException (typeof(FormatException))] or even Assert.Throws<FormatException> (() => Int32.Parse("abc"));