I'm sorry, but this is just another form of ignorance to a serious problem. She's not going over and flicking them on the nose! No one with a phobia willingly puts themselves in a situation where they're exposed to their fear. Keep your distance?! What do you do when you're standing in close quarters waiting to get into a show and you look over and the person next to you is carrying their chihuahua? It's not about a pitbull chasing you down the street; the mere presence of a dog (or threat of same) is enough to set most off.
I'm very lucky that I got over that particular fear, but I still remember how it felt.
Considering how rare dogs in the park are, I do think, "Just keep your distance" is perfectly valid advice. The only dog I've ever personally seen in the parks was a Disney K9 Security dog.
The phobic person has no more right to be standing in that line than the person with the seizure-sensing chihuahua (or whatever it is). As long as the dog is behaving itself, then all the phobic person can do is try not to go near it.
Asking a person with a genuine medical need to go without their dog would be unreasonable.
Similarly, people with dog allergies can't ask people with service dogs to leave the restaurant. All they can do is ask to be seated as far away as possible, or choose to eat at a later time.
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Anyway, with regards to the person who said they "didn't look disabled"...
Here's a link about a service dog who helps a person with a non-visible disability and an explanation of what she does for the person.
http://www.thatcutedog.com/job.html
You don't look disabled.
Lots of disabled people don't look disabled. Examples of hidden disabilities are: deafness/hearing impairments, seizure disorders, diabetic disorders, chronic pain disorders, neurological disorders, and more.
What does Raelin do for you?
Raelin has many tasks she does that help me. Some examples are momentum pulling (helping me walk), balance and counter-balance, retrieving objects (either by name or as indicated with a green laser pointer or a pointing finger or a tapping toe or other such indicator), waking me up in the morning and physically pulling me out of bed, and more.
http://www.thatcutedog.com/job.html
And a picture of Raelin in Disney!
I don't know this man's story (the picture was posted on TripAdvisor), but look! He's actually got a chihuahua!
And this is Timmy.
http://www.youngsfunnyfarm.org/timmy-s-page
He was both a therapy dog (no legal rights) and a service dog (legal rights). He helped control his owner's narcolepsy, and made it possible for her to become independent. He also volunteered along with his owner at Ground Zero post 9-11. And they visited Disney World together!
This adorable little boy is autistic, and has an equally adorable service dog:
http://dizfanatic.com/disney_travel_with_service_dog.aspx
And finally, a group of disabled military veterans and their service dogs:
http://www.patriotservicedogs.org/about/