Here's me with my OT hat on: Reading requires visual skills of convergence (moving the two eyes to come together and focus on a near point target; aka "going crossed eyed" when done to the extreme) and near acuity. Children are naturally far sighted, sometimes up until 5 years of age, so near acuity is typically not as good. Because most kids aren't reading before 5, the farsightedness is not an issue. But when a farsighted kid reads early then it *IS* an issue. It makes reading difficult and puts a strain on the young eyes.
Convergence also develops over time and is sometimes an issue, called "convergence insufficiency". This means that the eye muscles have difficulty holding that position so that both eyes are focused on the near target. Sometimes younger children with poor muscle development have difficult with this. If the child is reading then the issue is evident and a problem. For the typical child, the convergence insufficiency may not be noticed or problematic until later in school when reading and writing.
I'd say that doctor's comments were perhaps backwards. She seemed to imply that the reading caused the need for glasses, but perhaps it is more likely that the glasses are needed to make reading easier. Glasses for near point vision typically reduce eye strain.
What does KG say when he reads with and without the glasses? Does he notice a difference? Why did you take him to an eye doc in the first place? Was he having problems or just a routine checkup?
I had a three year old that I was treating who I felt needed glasses and sure enough the eye doc agreed. The preschool staff were shocked that the little guy kept his glasses on all day. Of course he did! He needed them and he knew it, even if he couldn't articulate it! And the great thing was that once he got his glasses he all of a sudden could sit at the table and do the fine motor and visual motor stuff that he wouldn't do before!! Imagine that!
I agree with others. If your ex disagrees he should get a second opinion. And if KG says the glasses help, end of discussion. He needs them!