its true, to a point.
Dogs mouths tend to be open a great deal of the time. More air circulates through the mouth and tounge it kills most microbes and bacteria that like darker, damper conditions. They also dont eat the crap we do, they dont get as much stuff stuck in there teeth. If they only eat hard kibble they will have a cleaner mouth than yours.
Actually on discovery channel Myth Busters show they did a test on dogs mouth compared to humans and the dog was something like 65% cleaner than the humans
Addition Info: Dogs Saliva have anti bacterial make up that clean the teeth and tounge when ever they begin to salivate. Its not a wivestale actually, its a documented treatment of the poor and homeless (street beggars) in biblical times. Those people too poor to get medical treatment would let the street dogs lick there wounds in order for them to heal... not gaping wounds but little cuts, scrapes, soars, blisters. NOW a days we have more antiseptic enviroment, those people were hardier than us. We probably shouldnt let dogs lick our wounds.
CATS on the other hand have Extremely dirty mouth, worse than ours. I would never let a cat lick a wound. Its due to the specilized tounge hairs and the make up of there teeth. Also there diet is more rodent based and therefore get more germs from there food.
9 years as Shelter manager, wildlife rehaber, raising orphaned animals, investigator for animal abuse\neglect and years of owning,training, breeding many types of animals.