Here's what I would have done. I would have left her wet clothes laying out somewhere. I wouldn't have put them in the dryer because she may not have put everything in there in the dryer. I don't dry my underwear or certain shirts or jeans in the dryer. No one else knows that but me.
Now, if I HAD put her stuff in the dryer and she chided me for it, I would have apologized. But to the part about it not being my floor, forget it. I would have point blank said, "That doesn't matter, period." And I would have ignored anything else she had said from that point on.
From the first scenario, if she had fussed for me taking her stuff out of the washer so that I could wash my clothes, THAT is when I would have told her that she didn't have dibs on leaving her clothes in the washer after the machine is finished. If she doesn't want people to take her clothes out, then she needs to be punctual about coming and taking the clothes out. And if she started the stuff about it not being your floor, again, I would told her that it doesn't matter which floor I wash my clothes on and ignore the rest.
Unless it is written in your contract about which washers you use, she has NO RIGHT to say this to you. She's just being crabby and rude. She's an old lady, and nothing you say will get through to her. The only thing that will teach her a lesson is for you to take her stuff out of the washer. Maybe THEN she'll set the alarm clock to come get her own stuff and put it in the dryer.
That being said, if I were you, I would bring a book or paperwork to work on and sit with your laundry. This way you can make sure that she doesn't mess with your stuff if you end up back on that floor.