Yes, it is, since there is no way of knowing absolutely whether each person had one dog or several, no matter which sentence you use. This is a different case, since the number of dogs per person is not so absolute as the number of lives per person, but anyway, it will have to be fitted into context that makes the dog/owner ratio clear.
1. Most people there had a dog.-- This is pretty clear: probably one dog per person...per couple?
2. Most people there had dogs.-- This is not so clear. What does common sense tell us? Well, some readers would think a dog apiece and some would think otherwise.