Doesn't necessarily need to be a document - it is a term for an alternative source for the additional material in Luke and Matthew that isn't in Mark. It could be oral tradition. There is no problem with the notion if Q as there need to be source material for what is in the gospels unless you think that the gospel writers simply sat down decades after the events and made up their accounts completely from scratch.
Indeed the title of this thread is about source material - the OP suggesting that source material is eye witness accounts.
I think that's probably what happened with Matthew: as an eyewitness he sat and wrote from scratch having probably written quite a lot down in note form already.
B. Ward Powers (2010) in The Progressive Publication of Matthew: An Explanation of the Writing of the Synoptic Gospels, argues that people in Jerusalem were writing short accounts of the life of Jesus, which Matthew collected, and which were also collected and distributed by visitors from further afield. Luke then and Matthew then published their gospels around the same time, Luke also using other eyewitness accounts; this explains how he has some similar and some differing material to Matthew.
When I mentioned Q, I was thinking more of your inferred source for Mark. The reason I said the latter is causing knots is because you used it as a way to avoid the conclusion from Mk 4:2,33 that Mark had quoted from Matthew. Then you implied it must exist, because Mark must have had a source. You said that source couldn't be Matthew because Mk wouldn't have left out Mt's extensive sermons. That seems a weak argument, because of course he could have left them out.
But another reason for thinking that Mark used both Matthew and Luke is the order of the pericopes. If Markan priority is true, then whenever Matthew deserted Mark's order, Luke always took it up at exactly that point. And whenever Luke deserted Mark's order, Matthew always took it up at that point. This happens dozens of times (I'll check how many), which would be a very big coincidence. It's easier to say that Mark had access to Mt and Lk, and whenever he came to material in one major gospel that he wanted to skirt around, he switched to using the other major gospel, or his independent source from whom his 4 unique pericopes come.
No it isn't. You really can't get away from the fact that one of them copied the other. Matthew and Mark are not independent.
But sometimes there are significant differences, explained only by their having different sources. In the scenario I just mentioned in this post, Mark would have used Luke's account of the same story instead of Matthew's. The Gaderene demoniac would be a good example, since Mark is almost the same as Luke there.
I hope I'm not coming across as being tied in knots. My view is that of Powers in the above book, which I'm reading.