OP here - thanks everyone for the replies.
Just to clarify, the student bags were not checked over by school staff either. These are older kids, many of who packed their own snacks so there was zero adult oversight on what was in their bags prior to the security check. The kids had been told to bring a snack to eat on the boat ride but I don't recall any specific instructions saying no snacking allowed between getting off the bus and getting on the boat.
I didn't allow the kids in my group to eat on the grounds but I did see at least one teacher in the group chewing gum and another teacher ended up having her group sit off to the side in the shade to snack. (It could be there were special circumstances for the teacher allowing her group to snack but I can't imagine a reason why the other teacher would be need to be so obviously chewing gum.) I did offer the option to my group that we could go back to the entrance area and try to find an area where snacking was permitted.
The Mount Vernon web site specifically says no food or beverage other than water is allowed:
http://www.mountvernon.org/plan-your-visit/tips-for-your-visit/guidelines/bag-inspection-policy-prohibited-items/