Early on in Manchester by the Sea, there are at least 2 scenes of people mentioning Lee's name in a way that makes it clear he is known around town: "That was THE Lee Chandler" or similar. It makes sense that people would know him; it's a small town, and he was involved in a life-changing event that caused him to move away. This would explain why people seem surprised to see him or hear from him.
However, when the hockey coach mentions his name, one of the other players, a friend of Patrick's, says "you know it's all bullshit, right coach?"
This line seems to say that there are rumors about Lee that some people don't believe. But I'm not sure if the movie ever says what the rumor is. The fact that his children died in a fire would have been well-known fact; not something left to speculation.
Was the rumor that he was responsible for the fire? Which would mean that it was actually true, and the hockey player friend was just incorrect? Or were there incorrect things that people believed about Lee?
Or does the movie simply not address this, leaving it up to audience speculation/interpretation?