RE: Songwriters knowing music theory, I don't know how traditional composers think of music theory but I tend to think of it like a box of tricks. It seems to me that, although Lennon/McCartney, Jagger/Richards, Morrissey/Marr etc. didn't know music theory how a professor of music might imagine it, they've all got favourite chord progressions, harmonies, ways of phrasing a melody, other tricks, basically knowledge about music: they just don't know what the name is for what they're doing. I think that's the only difference really. Well, your music professor's knowledge is obviously going to be more comprehensive, but it's not like they're trying to conceive the whole idea of a chord progression from scratch every time they write a song.
Inevitably, these people have all written so many songs and tried so many chord progressions, or found chord progressions they liked playing other people's songs, or bumped into some guy who's said, 'Hey, have you tried this chord?' that they already know what's going to sound good, they're not stumbling around half as blindly as they might have you believe. Fair enough, they'll occasionally do something by accident, and decide 'Wow! That's so cool!' and it gets in a song, but the fact is that these people were writing so many great songs in such a short space of time that they couldn't possibly rely on doing something incredible by accident every time. When I read things about the early Beatles I'm always struck by, considering Lennon claimed to not know anything, they seemed to spend the whole time asking anyone who'd listen everything about music that they possibly could!
Basically I think the whole idea that songwriters don't know music theory is essentially a myth, that spreads because people's own ideas of what music theory is are too narrow. I think it's perpetrated by the songwriters themselves to an extent, in the way that it's quite endearing and makes them all sound especially brilliant, when in reality they know all the tricks, they just don't necessarily know what it's called. And of course it's a great story for the media too.
You can see it in the media's favourite football managers too, Harry Redknapp, Brian Clough etc. claiming tactics are a load of nonsense when it's only really because they've got a narrow definition of it in their mind - they're (were for Brian) still out there coaching the players every day telling them what to do in different situations etc. and actually they know exactly what they're talking about, they're not winging it at all.
*Rant over*
