No, no, that's not how it works.
To be false, a statement must first say something. The falsehood of an idea is established by reference to a body of knowledge, knowledge contradicting the idea. When you know that a thing isn't so, then you know it by reference to your awareness of what is. Arbitrary assertions, lacking evidence, provide no such awareness, so they do not even reach the level of being false.
Arbitrary ideas are not propositions at all, they are pseudo-propositions. They are words with the linguistic form of a proposition, but without cognitive meaning.
The rational response to an arbitrary assertion is to dismiss it, that means do not assume its truth, do not assume its falsity, do not take it as a hypothesis, do not try to refute it, do not pass go, do recognize it as fantasy and turn your attention to reality.
For an idea to be disproved, for it to qualify as false, you must already accept and adhere to the principle of dismissing the arbitrary. Otherwise, there can be no disproof and nothing can be established as false (or true). The refutation of any claim presupposes that the arbitrary is not logically entitled to a refutation, that it has no cognitive standing. Otherwise, there is always the comeback "maybe you erred" or "maybe you're dreaming all this".