A while back, I (a solo 64 yr old female, 5'3", 135#) wrote a post about men approaching me while I was living/traveling in my van. It was deleted by the mods because it was perceived as male bashing, NOT my intention. But guys, you know how we ladies are taught from a very young age to be careful of strangers? Yep! Men have approached me in parking lots and asked to see the inside of my van. I have been invited into their vehicles. Total strangers. I'm never outright rude but neither do I encourage that kind of close contact without getting to know a person first. This is my home! Would you (male OR female) walk up to someone's house front door and ask, "Can I come in and see your home?" Really?!
I no longer live in my van, in fact I sold it a few months ago and live in a fifth wheel now in an RV park where I know everybody. But right now, as I write this, I am traveling in a rented Roadtrek (it is beautiful!). Two days ago, a thunderstorm blew up, raining sideways, flooding intersections. I pulled off the road into a parking lot in a commercial area of a city, waited it out. When the rain let up, I got out to have a smoke and a car drove by me, stopped in front of me, a man got out, walked towards me, I put out the cigarette and started to get back in the van. He shook his head no, pointed at me, and approached me asking if he could see the inside of the van. He was about my size and I figured I could take him down if I had to. So I opened the rear door. No way he could've gotten in because the sofa runs across the back but he could just see over it. Was I afraid? No, but I was cautious and maintained more than an arm's length distance and a strong stance. I may have been less defensive with a woman, who may have been just as much of a threat, but there is a physical strength factor there.
Does this mean I never speak to strangers? Not at all. But my radar is always on. And the great folks I have met far outweigh the few iffys.
There are a number of reasons why the woman was rude to you, OP. But I write this because we all should respect others' spaces and keep in mind an uninvited approach, especially in a parking lot, may be perceived as a threat.
Btw, this Roadtrek, 2014 210 Popular, is luxury, for sure. Had a number of RV's in my lifetime and this one is solidly built, well thought out floor plan, and as easy to drive as my old E-150, so far. I rented this to take my seven year old grand daughter on her first "camping" trip. This is more like glamping. It also gives me a chance to consider whether I would buy one of these (an older model) because I live by KISS and this doesn't qualify but it has AC. So far, we've stayed in RV parks on our way to my favorite primitive place high in the Rockies. We'll see how my little city girl companion manages without her phone and tablet and all that jazz. Wish me luck on that
Best wishes to all!