I suppose it depends on the game, but for the most part this is spot on. Even something as far from combat as Scrabble uses both A-R-R and R-A-R. It just depends on when you start the sequence. You could argue that acquiring random letters is the first step in the sequence, followed by laying down a word as your action, followed by result of scoring points. You could also note that any word you lay down is action, followed by the random acquisition of your letters, followed by the result of how it impacts your opponent on the board.
In the end, though, a good game can be accused of having both A-R-R and R-A-R because in it could still have a random component counterbalanced by the player's strategic decisions as well as the opponent's strategic decisions.
Just for the record, the CGE guys spoke better English than many of the supposedly native-English speakers I grew up with!
I guess that from their perspective of the market, ARR must look pretty archaic. I still think it's the right choice for my game, but I definitely see how publishing an ARR game could impact negatively for them across their entire portfolio.