Sorry to bump this, but it got no replies and I'm having the same issue.
Currently CCC 13.1.
I read in this guide (http://www.rcrncommunity.com/vga-guide/ati-amd#ccc) that it's important to set the same values for AA and AF you made in the CCC in the Skyrim settings (either via the launcher or the .ini itself). However, that makes me think that's just because they don't override properly. That's like saying something will magically fly into your hand as long as you go pick it up.
Are you using SKSE? Because I'm wondering if, even though the game still uses the TESV.exe to run, maybe launching it with skse_loader.exe is confusing the CCC?