What I've heard from old Hollywood types is that the studio pulled strings. Ford wanted him to join Oh So Social with him and Wayne chose his career.
If you want to write a fascinating book, check out the relationship between Ford and Wayne. Some of the guys who knew them both are still around, but probably not for much longer.
The last bio I read of John Wayne, "John Wayne, American," did not come down conclusively on whether he "ducked" service. The authors concluded that he, indeed, had legit exemptions, but that like many others he could have lied about them or concealed them if he wanted.