Paul McCartney deliberately avoided learning how to read music, but he understands music theory just fine. They are two different skills. It's quite clear from The Beatles' music that they know about keys, chords, etc.
For example, McCartney tells a fun story about The Beatles traveling across Liverpool to learn a single B7 chord in their early days: https://www.youtube.com/shorts/_r5B1AhP1Fo
I hear your point. I wouldn't personally consider someone who knows what a key or a chord is to be well-studied in music theory. Surely even Kurt Cobain understood which power chords he was playing, for example.
I was referring more to being well read in music theory in the academic sense. I am doubtful McCartney ever picked up a book on the subject. Traveling to meet someone so they can show you how to position your fingers so you can play a B7 chord is a bit different than that in my opinion.
For example, McCartney tells a fun story about The Beatles traveling across Liverpool to learn a single B7 chord in their early days: https://www.youtube.com/shorts/_r5B1AhP1Fo