When people point to statistics in response to "lived experiences" they're not denying that it ever happened. They're refuting the claim (implicit or explicit)

When people point to statistics in response to "lived experiences" they're not denying that it ever happened. They're refuting the claim (implicit or explicit) that this experience is representative of some broader whole. The plural of anecdote is not "data". For instance if someone says they experienced X event, but statistics say that X only happens to 1% of people it's entirely fair to bring up the fact that empirical evidence suggests it's a rare occurrence.