Private meetings are not supported
If someone books a room in a private meeting and Meat does not have write permissions on the room's calendar, Meat ignores this booking and displays the room as free.
I believe this is because you cannot see any attendees of a private event unless you have "Make changes to events" level of access or higher - see https://support.google.com/calendar/answer/34580?hl=en-GB .
For reference, our meat google user has "See all event details" permission over the room calendars. It can see the private event exists, but cannot see any details of the event other than its duration.