I think it's weird that when there was a chair available where she wouldn't be sitting next to anybody, she wanted to sit in the chair right next to you.
I thought it was kind of weird, too. And uncomfortable. I'm all for chatting with random strangers, but this was just...strange.
I am glad to know that I wasn't rude.
I also think that chairs are for people and not things. I think you were rude.
When I am going to put my bags or coat on a chair, I always move it if I see someone looking for a seat.
I do that, too. I did mention in my original post that if there are only 2 empty seats, I wouldn't try put my things on a chair and would move them if I saw the number of empty seats diminishing.
I think the only way the situation could possibly have been more uncomfortable and strange would have been if I was the only person in the waiting room.
The woman I'd been chatting with before the second woman came in did not say anything or make any sort of expression indicating that she thought the second woman was strange or weird for wanting That Seat. Then again, she may have just had a very practiced neutral face.
I've had time to process it and still don't really think I was rude. And like other posters said, weird =/= rude, so maybe she was just an unusual person who wanted her preferred seat - which leads me back to wondering if I really was accidentally rude.