It isn't that AA and AVRT don't "play well together", it is more a matter of completely different paradigms. There are points that oppose each other, and within each paradigm lie the reasons why. There is no problem with anyone doing anything they want, and if it results in the desired result for them, then fab.
Although I do not "use" either per se, I have studied them both extensively. I do think that for purposes of discussion it's important to know why a point or strategy is in place within a given method. It's like if I'm discussing Christianity and I tell others, with full authority, that hey you can just decide what God's word is, or you can choose to believe in Heaven but not Hell, or whatever...um, that's not going to be well received. Sure people do it all the time, and it works great for people...but technically, it's not Christianity without certain basic tenets. Same with AA, AVRT, SMART, Celebrate Recovery, Lifering, WFS, etc. Doesn't mean it's not okay to individually interpret, to blend, to pick and choose...but in my opinion, it's important to truly understand the basic tenets of a method because if I choose very opposing methods, for instance making a BP but continuing to live without a drink a day at a time, then I might find myself frustrated or unsuccessful without really understanding why.