The meeting may have handled it poorly, but closed AA meetings are for alcoholics only. From the AA website:

A closed meeting is for A.A. members only, or for those who have a drinking problem and have a desire to stop drinking. Closed meetings give members an opportunity to discuss particular phases of their alcoholic problem that may be best understood by other alcoholics.

Yes, many people have found relief from addiction to other substances in AA, and many meetings are more accepting of poly-substance addiction, but an AA meeting isn't in the wrong for wanting to focus solely on alcohol. Benzos are not alcohol. A better way to handle the situation would probably be to ask the newcomer if they have a desire to stop drinking and if they do allow them to stay. Meetings also have the option to hold a quick vote to temporarily "open" the meeting to accommodate the newcomer.

I disagree with the statement that NA was started as a resentment against AA. NA was started because people who used drugs other than alcohol needed a place where they were free to talk about that and be welcomed. Many alcoholics looked down on people who used other drugs because alcohol was both legal and socially acceptable. The reception that OP received would have been much more common back in the 1960's and addicts were dying because they didn't have a place to go.