You were completely in the right to protect your pup.
And the method that the woman's trainer has her working on is counter-conditioning. But she doesn't have a very good trainer because counter-conditioning isn't a technique that you give someone a crash course in and then just let them loose. To be used effectively, it is something that a skilled trainer would employ after much time spent understanding the dog's triggers and reaction threshold. And even then, it starts in a very controlled environment where as many variables as possible are controlled by the trainer handling the dog. Without free manipulation of those variables (namely the distance and position of the other dog) it doesn't do much to actually teach anything.
In short, it is a legitimate technique, but it is being used in an ineffective, shoddy way in this situation.