I think that's correct for some assertions. When a statement is "this is always true", then a counterexample is all it takes to disprove it. On the other hand

I think that's correct for some assertions. When a statement is "this is always true", then a counterexample is all it takes to disprove it. On the other hand, if the statement is "this is not always true" then an example of it happening is as you said - the example does not counter anything.