Is Luke Bryan the Only ACM Entertainer of the Year That Has Not Won a CMA Award?

If I'm wrong about this, please let me know, but I'm doing some research for a top-secret Luke Bryan project (it has to do with us giving away tickets to his St. Louis concert) and I've come across something interesting. From all of the data that I've found, it appears that Luke Bryan has never won a CMA Award. He's been nominated for several, but he's never won. Does anyone else think that it's odd that an ACM Entertainer of the Year has never taken home a trophy from the other big award show in country music?

I don't know a lot about the politics of country music. I couldn't tell you the difference between the Academy of Country Music and the Country Music Association, other than one of them holds their awards show in Vegas. I do know that winning top honors at either the ACMs or the CMAs is a big deal. Only the best of the best take home those awards, so it seems strange that an artist could win one award show's highest honor, but never win anything from the other one. Has this ever happened before?

If you know of a precedent for anything like this, please leave a comment and let me know.  By the way, we'll be announcing this top-secret Luke Bryan project that I'm working on the morning of May 13. That's all I'm allowed to say. In fact, I've already said too much...