Assuming X is true, that implies Y. We don't think Y is true therefore we now doubt that X is true, is a very standard thing to do in math.

Yes, but the title suggests that "[method] solves NP-complete problems", and sounds kind of like "Quantum-Physics-related trick solves NP-complete problems".

Moreover - it doesn't even solve NPC problems conditionally, but that show that "in principle" they should be / would be solvable.