Despite what old wives' tales suggest, the average dog's mouth isn't cleaner than the average human's. Dogs suffer from different types of oral hygiene problems than people do, but that doesn't mean those problems don't exist -- they're just caused by different types of bacteria, like the periodontal disease-causing P. gulae.
The actual number of germs in a dog's mouth is approximately the same as in humans, and in some cases, the bacteria are even closely related. For example, both humans and dogs have bacteria in the Porphyromonas family, which cause periodontal disease. While the human mouth is populated by P. gingivalis, though, dogs have P. gulae. While dogs are not prone to all of the same oral health conditions as humans -- tooth decay caused by sugar consumption, for example -- their mouths are still filled with bacteria.