If I make a claim, the claim is (to adopt your parlance) true or false - correct.
But if you do not/cannot know that as a matter of fact, then it is perfectly reasonable to evaluate the credibility and history of the speaker. If the only source of information is a non-credible source we have no reason to believe the claim, which is all we can do, whether or not it is true.
If the president of the united states tells you an asteroid is about to hit the earth you are likely to take them more seriously than a homeless person on a street corner. But you are correct, in both cases it either is or is not going to hit it.
The appropriate response you are looking for is asking for other sources of evidence. Your comment is just bad epistemic noise to try and undermine a critique.