... opinions vary.

On the "leave the dog alone" side, the rationale is that the dog is working and needs to pay attention to the human and his/her particular needs. In the case of a diabetic, it needs to detect a diabetic emergency; a dog for the visually impaired needs to guide its owner without leading the person into obstacles, and so on. In the case of a dog for people with balance issues (as a Great Dane is often used for), it needs to be switched on to detect even slight changes in balance indicating a potential fall. Some handlers don't even like you to talk to the dog because it's still a distraction.

On the other end is like the poster in one of the threads above. Some handlers acknowledge that distractions are an inevitable part of life and so the dog needs to be able to handle it while still doing its task ("walk and chew bubble gum" so to speak). In that case, even if they don't necessarily encourage interacting with the dog, they accept it.

This lady may have been on the overly sensitive side, or may have lied about the dog in the first place just to get it in the park and kept up the story, or may have just been tired from telling people to leave the dog alone. Who knows.