I agree that with post-1700 profiles, family stories or family history is enough reason to create a profile. With pre-1700 profiles, of course, reliable sources are required--see https://www.wikitree.com/wiki/Help:Pre-1700_Profiles#Cite_reliable_sources . Family histories are unlikely to meet that standard.
But you also mentioned talking to people. Don't forget that oral traditions count as evidence! (They are, of course, fallible, but so are written sources.) Ideally, your reference would give enough information for someone to start evaluating the credibility--the source (and the way they knew about the event), how you know about it (did you take notes at the time? are you relying on your memory of what they said?), etc.
This is obviously relevant for the recent past. (My aunt's story about my father's birth supports his being her sister, even though the state doesn't have a birth certificate for him, for example.) But family traditions may also be relevant further back in the past. See, for example, Annette Gordon-Reed's Thomas Jefferson and Sally Hemings: An American Controversy for a careful use of a combination of family tradition and documentary evidence.
