I can vouch for this. For some reason, people are fixated that one has to personally witness something to know anything - this really isn't the case.NPCs you've been nice to treating you as a DIK is presumably because people gossip, so even if you're nice to them they know the MC does a lot of DIK stuff elsewhere?
As a person who moved schools every 2-3 years growing up (my dad was a diplomat, but army brats etc would tell you the same), I can confidently say that within a week at a new place I'd know exactly who had what rep, who the jokers were, who were bad losers in sports etc. without having to see it myself. Heck, as a 6th grader other 6th graders would tell me who the sluts were in the 12th grade before I'd even talked to a single 12th grader.
Knowing someone's reputation doesn't require being an eye-witness or even knowing what they specifically did to earn it. E.g They'd say "watch out for him, he likes to tell on people" and that's enough. They don't recite a list of examples.
Some info may prove wrong eventually but impressions are already formed.