Counterexamples do not imply the inverse of the original claim is true, just that the original claim may not be a universal truth. (And of course, the OP never

Counterexamples do not imply the inverse of the original claim is true, just that the original claim may not be a universal truth. (And of course, the OP never claimed it was, your claim of "literally nothing" is more akin to making a universal claim.)