Being a music teacher who's strong suit isn't reading music, I can tell you a few things. McCartney understands everything functional about music theory. Not reading the notes on a page is not a matter of pride, it is a matter of not really needing to. If a person is exposed at a young age to a competant teacher, (rarely), then reading music is no more difficult than learning to add and subtract, or learning to read. If not, talent, a good ear, ton's of enthusiasm, and a competetive peer group will do the trick just as well. I went to a few music teachers when I was around 15, and they were only capable of playing, and did not teach well (even though one had been well known). I played by ear for 8 years, doing albums, tours, sessions, etc, before studying with a great teacher for 4 months, in which I learned more about music than in the previous 8 years. What is necessary, is to know enough about music to communicate with other musicians and not feel stupid. I have taught my students enough about music to speak intelligently with any caliber of musician, without fear of embarrasment, even if their own ability is barely average. If I was going to be a teacher for a while, my goal was to be the teacher I couldn't find when I needed one. Thanks to Mr. McCartney for all of his great melodies, which are a permanent part of my musical "education".
