When I went to the grocery store, the most interesting thing that happened was that I parked next to a convertible with two very well-behaved dogs, sitting calmly in the back seat.
I don't know any dogs who could show that much restraint. Especially considering all those people walking by with bags of meat and cheese and ice cream. The dogs I know would have bolted like bandits and made nice with all the customers coming within a 20-yard range.