I think many people could benefit from AA who have a drinking problem but may not be "alcoholic" - that seems to just be a label to me.
One thing I learned while doing my psychology degree is that the "disease model" of an Alcoholic (widely believed) is simply not true. The idea that if someone has one drop of alcohol, it will biologically compel them to binge. It's psychological, not biological. I know this is not the popular view, but it has been proven in countless studies. If you give an "alcoholic" a drink with NO alcohol and tell them it contains alcohol, they are more likely to binge then if you give them a drink WITH alcohol and tell them it contains none. What does that tell us? It doesn't mean the problem is not real, but it is psychological and not biological.
Thus I would have no problem attending AA and saying I'm an alcoholic, because it is a state of mind. AA is a way of meeting other people and having support for living an alcohol-free lifestyle.
I don't know if it's acceptable to just say you have a drinking problem. That's more accurate anyway IMHO. And nobody is going to argue if you got a DUI that you don't have a drinking problem.