Dogs have cleaner mouths than humans.
Most dogs do not brush their teeth twice a day or floss, so no, their mouths are not cleaner than ours. You won't find humans eating rubbish or licking out of toilet bowls, either. It is true, however, that the healthier the dog, the cleaner they are. It's believed that this myth comes from the fact that dogs' wounds heal after they lick them. It's not their mouths are especially clean, it's just a similar practice to us washing a wound to prevent infection.