If your meeting absolutely positively must happen on a known weekly no-meeting day then there's really only three cases I can see:
1. You are bad at planning
2. You are bad at communicating
3. Something really, really bad happened and people will understand breaking policy
There's a big difference between "no meetings ever" and this.
Sadly there is a particular type of person who discovers the day that nobody is supposed to go to meetings is the day when everybody is free and the meeting rooms are available. And then starts scheduling meetings for that day.
This is the same kind of person who discovers that people, and rooms, are "available" from 12-1pm, and 6pm-
After too many days of back-to-back meetings from 10am to 3pm I've taken to creating a repeating lunchtime meeting with myself. Then I discovered the people who don't care if you're available or not...they consider themselves important enough that you'll drop everything for their meeting.
All meetings are optional - it just depends what you're prepared to pay for missing them.
In this case, I'd say there's no/negligible cost to missing the meetings on a no-meeting day, unless the entire group of people have decided that it is worth breaking the no-meeting rule. Of course, you should let people know that you won't be there in advance...
There's a big difference between "no meetings ever" and this.