Fresh from the Dairy

Like in most Albertsons stores, the dairy department here spans most of the back wall of the store. Surprisingly, this store had a dairy walk-in case added at some point, rather than just having the milk in an open-front case like most stores of this age do.

Am I the only one who thinks "Fresh from the Dairy" sounds odd? I know that a dairy can refer to the place where cows are milked, but in the context of a store (and, at least in my opinion, in normal conversation) it's generally used to refer to the milk products themselves. Or maybe I'm just crazy...