I've used a stroller on 4 separate trips, and have never had a problem. I use a backpack as a diaper bag,(diapers, wipes, disposable change pads, sippy cups, etc) and leave it in the stroller. It's all stuff that can be replaced if it HAS to be. All of my other valuables stay with me in a small purse that I carry everywhere. Strollers are often relocated by cast members, so don't be concerned if it has been moved.
The towel idea is great! I usually just have a bright colored scarf tied to mine to make it easier to identify.
I can honestly say that WDW is the only place that I've ever been that I feel comfortable parking the stroller, and walking away. I would never do that at the mall or any other theme park I've been to.
Have a great time!