First, socialization isn't just about "getting to know" or interacting. It's also learning to be appropriate in a situation without interaction (like taking your dog to the vet and NOT having them approach every dog in the place or bark because he can't play with them). So I suspect that is what the trainer was saying when she says she "takes them anywhere and everywhere to get the socialized".
I don't let my dogs socialize with strangers. Unless I know the owner and/or dog, it is strictly no interaction.
To me, it is not worth the risk. I've seen too many people who claim to be dog knowledgeable do really stupid stuff. I've watched dogs lunge/snap while the owner is stating they are "friendly". I've watched dogs ignore their owner while the owner is explaining how they have complete control over the dog.
Just the other day, on another website, a woman was asking for advice for her sick puppy. Folks responded that it sounded like parvo and the dog needed to go to the vet's asap. The woman kept stating that her puppy "had all his shots". When the puppy was 3 months old, she took it to Petsmart and got several shots. The puppy is now 5 months old and has never received any additional shots. But she has the "vaccination record" that shows he's had all his shots. She absolutely refuses to comprehend that puppies need a series of shots to be protected. I don't want my dogs interacting with hers. If she doesn't understand the vaccinations (and is unwilling to learn), then what else is she screwing up.
To me, I am my dogs' protection. I take that very seriously. I control my dogs' interactions. I do not let doggy day cares or boarding kennels decide what dogs are safe for my dogs to interact with. That is my decision alone. I limit interactions to those I know - both owner and dog. Out on trails, I step aside and let other dogs pass at a safe distance. If the owner tries to let their dog interact, I politely say no.
This is all that much more important as my Cat-dog is extremely afraid of being attacked by other dogs. Any dog that is coming towards her is an attack in her eyes. Having others allow their dog to try to make contact just cements that belief. She is doing a bit better, but this will take years to overcome. And the most important training is for her to be around dogs that ignore her completely. So I have to be very certain of any dog (and owner) that she's around.
P.S. I always keep a copy of the pets' rabies certificates in the RV and vehicle. I also put my RV and vehicle's license plate numbers on the dog tags - if I'm somewhere without cell service and the dog gets loose, others can find me quickly in the campground by the plate number. I used to use the barrel tags and write down the campsite, but they never stay closed. With the plate numbers, you don't have to change it every stop. I actually have two tags - one with the trailer and suv plate numbers, and one with the motorhome plate number. I switch them out depending on which I take.
1975 American Clipper RV with Dodge 360 (photo in profile)
1998 American Clipper Fold n Roll Folding Trailer
Both born in Morgan Hill, CA to Irv Perch (Daddy of the Aristocrat trailers)