Puppy has mites...From parents?

There's not much information to go from, judging from your brief paragraph. So I'll just generalize.

This CAN indeed happen. When a dog has a poor immune system (it's actually uncommon for this to have a hereditary trait) and a T-cell deficiency, they are susceptible to demodex mites. It is generally rare to uncommon for this to happen, but it could, depending on the breed, diet, age, and health of your dog. There are too many variables for me to guess to give you the answer you need.

This link may help you though.

not this particular problem. certain types of mange can be passed from mom to pup if the mom has mange and the pups have a compromised immune system. BUT you state that your dogs are fine so I seriously doubt that is the case. Just to be safe, maybe you should take your dogs to a vet and get exams and health certificates for them with a current date on the papers (you did have them all tested before whelping and examined after birth right?) It would show that your own dogs are not infested with mites. I think maybe that the infected pup's owner kept it in less than ideal conditions and is now looking for a scapegoat or a free ride (with you paying their vet bills)

They are demodex mites and are passed from mother to pups most dogs have them and if they are healthy their bodies can cope with them, but if a pup has a low immune system for any reason (not necessarily inherited) it can get skin problems. This is what one of my chihuahuas had, Her brother had no problem at all. They usually grow out of it, I treated her with Front line + and it took about 2 or 3 months to come right. She has the most beautiful soft coat now! The vet told me that it is very common. It can also be caused by stress.

I advuise you to audit daily the condition of your young puppies!We never know when these mites may attack the helpless puppies. Maintain good hygiene to your pets. See a veterenarian if possible to have your pet check up. Have a lovely day!