There is nothing in any of the 12 Traditions that would have prevented her from reading the prayer. The Serenity Prayer is non-AA. The Lord's Prayer is non-AA, too. And, it's a secular religious prayer that comes out of the Bible. However, that group might ban the Bible, too. (Even though it was the primary book used by the founding members of AA, until the Big Book was written).
The groups could have said "It violates our own Group's rules"... the groups are free to establish THIER OWN rules.
I remember as a newcomer witnessing a similar situation that really made me want to puke and kick some old timer's butts... I was a couple of months sober, and a young lady came to her first meeting and they ask her if she'd like to introduce herself and "say something". She introduced herself and then said "I don't know if I'm alcoholic or not, but I do know that I'm a drug addict." And, she was ran out of the meeting.
On the flip side of that, near the same time -- I had attended an NA meeting (one of the original founding NA meetings in Southern California) ... I was convinced that I was a drug addict before I became alcoholic -- and introduced myself as "an addict and an alcoholic."
The NA oldtimers hit me with "did you ever fix heroin? did you ever slam dope? did you stick needles in your arm?" ... and my answer was "no." So... they ran me out of the meeting and said "go back to AA, you don't belong here!"
I did stop going to NA meetings, but I continued w/ AA. I had made a commitment to go to any lengths to stay sober -- even if I had to lie about something...
Unfortunately -- we've got to remember -- that inside our Fellowship are some of the sickest of the sickest people. "If" they were so healthy they wouldn't have landed in AA. What's more unfortunate is: AA provides a program to treat our alcoholism, to help us get well and to change our attitudes and perceptions.... and there are many in the Fellowship, some with many years of physical sobriety -- that still haven't figured this out -- so they stay sick.
I would encourage you to read Tradition Three in the 12 & 12... and then suggest to the group -- that "since the 12 & 12 is AA literature that you suggest that they read it." There is an interesting story in there about a person that the group didn't want to admit to the Fellowship.
Sorry about the long rant of an answer...