It's possible that they could pick up tapeworms or coccidia. I've heard that some dogs are more susceptable to tapeworms.
I read today that those cute wild rabbits

can have at least 5 litters a year with an average of 5 cute little bunnies

per litter. If a person has rabbits around their property how in the world could you keep your dog away from the scat from that many rabbits?
Who in the world can watch their dogs that closely every second they're outside?
I guess the answer would be to have the pups stool checked on a regular basis.