I think that, although there need to rules, empathy and exceptions always need to be implied where parents are concerned.
I'm head of performing arts at an independent school for 3-13s which, across the whole school, has 12 school shows a year (the children only eligible to be in a maximum of 3 each though, the year group/s vary!)
I set rules because it's important to have a norm that the majority will keep to. But, as I'm also a parent of the school and have never really seen my own children perform because I'm always backstage, I do have a lot of sympathy with exceptions and find that it's usually easy to accommodate if parents ask in advance. Examples include letting parents come to dress rehearsals because they can't make performances, secretly filming the show for a terminally ill parent and a parent on active duty in Afghanistan (the filming was illegal but I felt the reasons justified the risk), letting a fantastic actor with significant learning difficulties use a script on stage and letting parents sit on stage with very young or otherwise needy children who want to go on but are just too scared to do it alone. Part of me hates looking unprofessional but the rational side of me realises that it's a school and it's about education, acceptance and inclusion.
Maybe if this mum had spoken to the teacher before just turning up it might have been different. I still think they should have let her in though.