A fellah I worked with played trumpet for the CSO. Yeah, you know, big gig, playing with the world reknown... Anyway, he can read music, etc., but when it comes to playing something that he doesn't already know, CACK! On the other hand, my friends ex-boyfriend taught himself to play guitar from a young age. Took his dads guitar, and just did it by ear. After a few years his dad took him to a teacher who was blown away by how good he was. He was in his early teens. It took him years to learn to read music. But he can play anything by ear after hearing it once. So you're right, the abilty to read music only gives you an edge as a session musician. The rest is up to your soul.
ETA- After seeing Neil a few times interact with other musicians, I think he can read OK, but is so proficient that it just comes to him "by ear" (if that makes sense).