I agree with him in that if God was enough then recovery would only be for atheists.
If you believe in God, you can't follow His will and abuse alcohol on a regular basis at the same time. However, I do believe that anyone can turn to Him at any time in repentance, can ask for His help at any time.
If you're Christian, for example, the Bible condemns drunkenness as a sin so when people are telling you you are powerless and have a disease, something doesn't sit right.
Whatever your religious persuasion I doubt your God wants you to sit around drinking all day, every day. AVRT gets you to the point where you are no longer living the immoral life of someone who abuses their body and their friends and family via alcohol. Morality is something atheists, agnostics and religious people have in common. AVRT will work just as well for all three.
I think the FAQ is saying that a) Rational Recovery does not care what your belief system is and b) you should not think that 'finding God' is a treatment to addiction.