A dog's mouth is cleaner than a human's, which is why letting the dog lick your face, or your wound, is supposedly fine, even healthy. People repeat it to justify the slobbery kiss. The dog that just sniffed three bins is, apparently, more hygienic than you.
A dog's mouth is not cleaner; it is differently dirty. Dogs and humans each carry hundreds of species of mouth bacteria, and the two sets barely overlap, so comparing them as 'cleaner' or 'dirtier' is mostly meaningless. What is clear is that a dog's mouth carries plenty of its own bacteria, plus whatever it has recently been eating, sniffing, or licking, which, given canine hobbies, can include some genuinely unpleasant things. Most of it will not hurt a healthy person, but dog saliva can transmit bacteria like Capnocytophaga and Pasteurella that occasionally cause serious infections, especially in people who are immunocompromised. The 'healing lick' idea is an old folk belief, not medicine; you should not let a dog lick an open wound. So the face-licking is not a health treatment. It is a dog being a dog, with a mouth that is simply running a different zoo to yours.