I've heard that same thing. But I really don't think that the dogs mouths are much cleaner than a humans mouth.
In fact I would say the dogs mouth has to be much dirtier than a humans mouth since some dogs eat poop and they lick their private parts to clean them and the private parts are dirty.
There's no way in my opinion that a dogs mouth is cleaner than a humans. I brush my teeth everyday and use mouth wash everyday as well and I don't eat poop or lick my privates.
So I would think my mouth is much cleaner than a dogs mouth.