> no one has made my point,
> which is that musicians think differently
> than non-musicians-
That's just a matter of training. It's not that musicians "think in measures" because we don't (and I don't know anybody who does) - musicians are just used to phrasing musical ideas in the structure of a series measure. Most of the time it's an unconscious thing.
It's not a matter of knowing music theory (I've known quite a few great players who couldn't explain the concept of a time signature if you put a gun to their heads), it's really a matter of coming to an understanding WITH music theory. The attitude is sometimes expressed along the lines of , "I don't know why it works, but it works so I don't sweat it."
As for thinking differently, training in any craft is going to alter your view of the world around you. That applies to weaving, karate or playing the banjo.
Any musician is going to miss a note now and then. Perfection is an illusion. The difference between a pro and an amateur is that the amateur will freak out over a missed note and the pro will either ignore it or act like it was intentional.