In California (believe it or not) we have what is known as the Brown Act, and meeting in someone's living room is most definitely a criminal act.
Definitely not OK.
As for public meetings, unless it is an executive session discussing public employee bargaining, or pending suits, etc., it must be a public meeting.
I would record a public meeting no problem. Miniature sensitive recorders are widely available, now.
That’s for governmental entities. This is not a governmental entity, it’s a club at a university. They chose to make it a public event when they decided to use the university’s space and announcements to publicize it, but they could have held a meeting at a private location, not being a governmental entity.