My Blind Date Refused To Walk With Me In Public

I have a dispute with someone I met on a blind date. We had talked a good bit on the phone before meeting and seemed to get along well. We promised if it didn't work out, we'd at least be friends. But, when we met, she seemed very uncomfortable. At first I chalked it up to first date jitters, but then as we strolled in public (to/from the store, the restaurant, the sports venue) she refused to walk beside me. Not only did she walk behind me, but she was several FEET behind me - AT ALL TIMES. I urged her to walk with me, and she refused, telling me to "go ahead". By the third time I had asked, and her obvious reluctance to even stand near me in public view, I decided I must really be repulsive. I was going to end the date because I felt so disrespected, but when I tried, she changed the subject. So, I virtually shut down and wrote the date off. I went through the motions, barely talking the remainder of the date. She didn't even notice (not that she was talking much either).

To make a long story short, I eventually let this person know how I felt. She was supposedly shocked that I had perceived what I did. "I do this with everyone" was her response; usually coworkers, but also men she's dated...she claims none of them have expressed anything but minor annoyance. I didn't buy it, but she has insisted this is the case. Has anyone ever had this happen? Am I over reacting? Keep in mind, this happened from the get go - at the very crucial "sizing up" period when meeting a blind date. What else was I supposed to think?