Going back to the thing I mentioned earlier in the thread, "This statement is true" has similar problems to "This statement is false", though in some ways it's worse because it's harder to detect.
The core of the problem with "this statement is false" is that it is completely impossible to determine whether it is true or false; if you test to see if it could be true, it will fail that test, but if you test to see if it could be false, it will fail that test also. "This statement is true" is also impossible to determine whether it is true or false; if you test to see if it could be true, it will pass that test, but if you test to see if it could be false, it will also pass that test.
In a way, things like this are more dangerous because many people upon seeing that passes the "could be true" test simply stop there and assume that it's true. To be fair, I doubt anyone has been harmed by accepting "this statement is true" specifically. But in general, accepting that a proposition is true when it has not been properly demonstrated can easily lead to inaccurate beliefs, which can easily lead to harm. For this reason, I think its good to recognize the problem here so you are less likely to fall into it when it can be harmful.