Perhaps it's time that WDW put signage at the pools stating that there is no saving chaises/tables. If you aren't in the pool or otherwise active in the pool area, you don't have a seat.
There have been many situations where people have headed down to the pool, very early, placed some towels and even a book, on a bunch of chaises or tables that are poolside, and then gone on about their business, planning on returning to the pool later on. Sorry, but that's just not right. So...what should the lady who claimed it was her table done? Perhaps she should have left someone at the table while she went off to get food. But, I think that she, and her family, may have arrived at the pool, staked out a prime table with their unused pool towels, then gone and eaten their lunch at a nice leisurely pace, expecting that no one would be so bold as to encroach upon their previously staked out table. Sorry....wrong expectation. You go to the pool when you are ready to swim, or whatever. You stake out your spot, with towels or whatever. Then, if for some reason you need to leave the area, just leave some personal effects that will show that you have been using these seats and will be returning. There are times when you may be at the pool and then want to get a bite to eat..sometimes even bringing it back to the pool with you. That's fine. But to stake out a table then leave for an undetermined time and expect the table to be free is not right.
The Disney ships all have signage that states chaises/tables may not be saved. If you are not actively using them, then anyone is entitled to it. Should be the same at WDW.
Now, if you want to get really picky, let's discuss those people that take up about 6-8 chaises, then spread all their stuff all over the place. We were at BWV in August..it was brutally hot so we spent a fair amount of time at the pool. Well, almost every day, we had to head to the nether regions of chaises since those closer to the pool were taken. Not a big deal for us. But, because we had to take a second tier of chaises (all of two for the three of us), we had to wind our way through the belongings of those in front of us. We chose our chaises on the very end of the row, so it should have been easy to access them. There was basically only foliage next to us to our immediate right and the row of chaises to our left. But, those in front of us had their drinks, snacks, shoes, etc. all over the area that we had to go through to get to our chaises. At one point, when they had evidently had enough swimming for awhile and were stretched out on their chaises, we returned to ours, dripping wet (had just gotten out of the pool). Well, as we tried to carefully navigate through their belongings, my dd dripped on a book of theirs...you should have seen the look she got from the woman lying next to the passage area...my poor dd felt awful. Yes, I was a bit miffed as I said to my dd...'Try to be careful and not drip on other's belongings as you try to get back here....I know it's hard since the space for you is non-existent!!!'
If people would just stop and consider how their actions are going to impact others life sure would be nicer.
That towel leaving woman should have realized that just leaving a few towels does not 'mark' that table as hers. Sure, most people would see the towel and pass by. But the OP was perfectly within her rights to use the table. There was no way of knowing if those were towels that belonged to someone or had just been left there.