A broken-link checker visits each link and reports the HTTP status code the server returned. Two codes cause many false alarms. A 403 means the server understood the request but refuses to fulfil it. A 429 means the sender has sent too many requests in a given time, which is called rate limiting. In both cases the server answered, so neither on its own says the page is gone.
This guide shows you how to sort a report by code, check flagged links by hand, and make sure your own site is not turning away Google's crawler by accident.