I don't want to sidetrack this thread but I did look at the first site and they did describe a therapy dog much the same as I did. Perhaps you are confused on the certified part, hospitals, nursing homes , ect can I guess allow any dog to come in and call it a therapy dog themselves but most places require the dog to be certified and insured.
I did see where that site will apparently sell you a certificate for service, support, and therapy dogs without any proof that the dog was trained for such duty. Like the online Diplomas that are sold, guess if you can find someone that accepts them as real then they will work.
Most places I worked with in the past had a list of the pet therapy organizations that they accepted and I would never take my pet into such a place without having him insured. And you are not going to get him insured unless you have him trained and certified by a reputable organization.
It be interesting to know if anyone that has purchased one of these certificates actually got an airline to accept it.