What is also interesting to me about that interaction is what other people said to me when I mentioned it to them.
The young woman who spoke to me had an obvious American accent. We have several family members and friends who live in the States and so I mentioned this to a couple of them at the time.
A typical reaction was something like "Aww, that was incredibly kind of her to offer, someone raised her right."
but with the follow up "But yeah, I’d be internally mortified!"
Or "She's probably from the south or the mid west"
I don't really know how much US small town culture differs from the UK but I do remember the husband of my DH's niece (so nephew-in-law??) who is American and in his late 30s told me about one occasion when he went to a 7/11 near his old high school
"...and as I am walking to the door a group of like 10 high school kids from the rowing team from my old high school are walking out the door. I am polite and open and hold the door for them. They thanked me, and all called me sir, and were super polite and all of that.
Treated me how good kids treat an elder. That made me feel f***g old as dirt, especially since I was on that same team, albeit 20 years ago. And then I thought about it, and I could have gone to high school with their parents (assuming they had kids really young). That really made me feel old."
So maybe (and I'm hanging on to a thread here) just maybe, her offer was more to do with a sense of politeness for someone who was clearly older than her rather than thinking I really was in need of a seat..
Or, of course, that may just be me trying to rationalise what happened.