IMO, generally speaking, no one should ever have to deal with someone else's dog, cat, hamster, whatever running up to them not on a leash.  That's part of being a responsible pet owner and having a general respect for others.  
 
However, IN THIS INSTANCE, I think the lady's behavior was uncalled for and over the top.  If she was a regular customer and know that Uni was in the store, then it shouldn't have reacted the way she did or have been surprised.  I can understand if she had never been there before and Uni ran up to her, but she was a repeat customer!  

  I would have loved to have been greeted by Uni, but then again, I'm a dog person, more specifically a Yorkie person...not all people are.  (Although I can't imagine why not!?

)  But it was YOUR store and IMO, if she didn't like it, she could leave. 
I think this is a case of someone's irrational behavior and not an issue with a phobia.  Phobias are VERY real...even if you don't understand them.  (And I can completely understand someone being frightened and completely freaked out by dogs!)  I am really hoping that I just misunderstood the comment about "phobics being an irrational fear."  
