There are several organizations that match the name "Alcoholics Anonymous"
The IRS provides online Version of Publication 78 to search for eligible charities - http://www.irs.gov/app/pub-78/
Here are search results - http://www.irs.gov/app/pub-78/search.do?nameSearchTypeStarts=false&names=Anonymous&nameSearchTypeAll=false&city=&state=All...&country=USA&deductibility=all&dispatchMethod=search&submitName=Search
If you made cash contribution to any of listed organization - your contribution is deductible.
This system relies on the honor system and accepting responses is how the Experts that spend time answering you get paid. However, if none of the responses are acceptable to you, you don't have to accept them.
You are absolutely clear and I am not feeling as being cheated.
I wish you the best.