Back to overplaying - Keith Moon example is "The Kids are Alright": It's hard to discern what exactly is a fill since he never plays exactly the same beat consistently, but for the first minute or so of the song, the only significant fills are after the first line of each verse, with some fill-like activity on the last line of the chorus and transitioning to the verse intro. Then a busy bridge with a stellar fill, and back to playing it cool, etc. There are times when he'll come out of a line and completely skip the expected fill.
You can't really say that the groove of the song is the groove without that fill after the first line of the verse. Just like Ringo's groove on "Rain" isn't the groove without the fills. The melody of the song has the fills right in it.
I think one problem is the agreement with what everyone thinks of when "playing for the music". That description is completely subjective. As a drummer, I always seem to fight this in bands because 99% of the time, there is no musical arrangement for me to read. It is up to me to make it up on the fly. Of course...melodic instruments do not have this problem. I play what's in front of me on my stand.