As the discussion has revealed, "no public" is a polite way to say "only paying customers."
Further, if a bathroom has an Out of Order sign our job is to still ask if there is a bathroom available. Same if you just do not see one or even if they have a sign saying No Bathroom.
The client may just want us to observe how the associates respond regardless.
My posts are solely based on my opinions and for my entertainment, contact a professional if you need real advice.
When you get in debt you become a slave. - Andrew Jackson