You can't prove something by example, you can only show that the pattern holds for the examples that you've checked.
Yes, in math you can't prove things by example.
But in biology that's the only way you form knowledge.
Biology doesn't have axioms. In biology, proof is by induction. However philosophically unsatisfying that may be.
Proof implies a level of certainty that doesn’t exist in biology.
You can argue whether that’s interesting or not, but IMO it’s as much a proof as anything can be, and IMO it’s very interesting.
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.