Actually that's not a uncommon rule, it's part of the bowling etiquette list that only bowlers are allowed in the bowlers circle (settee area).
You use to be able to find the Bowling Etiquette list in the back of the old ABC/USBC rule books. So a lot of leagues included that list with their league rules.
Here's a example from the USBC 2016-17 Open rules:
"Rule 30. SETTEE
Only Open Championships tournament competitors and staff assigned to the squad in progress will be permitted in the bowlers’ settee area after the start of competition. "
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