I am a full time
scooter user. I have used a scooter at WDW for the last 5 years. I am currently using my second 3-wheel scooter. My first scooter was very light (98 lbs), and tipped over sideways twice in four years' full-time use (not at Disney). Both times involved turning while also on inclined pavement. My new, heavier 3-wheel scooter (168 lbs), which you could call medium-size, has larger wheels and seems much more glued to the ground.
The scooter tips that temporary users might experience are about the rider. You have to evaluate the physical abilities of the person using the scooter. If you wouldn't trust this person's reflexes or physical abilities to drive a car, then a scooter is probably not a good choice. A wheelchair would be the better choice. A scooter is, after all, a machine that can go a little faster than most people's walking pace. So there is potential for accidents if the scooter driver is suffering from diminished capacity.
The woman in the second post had vision and depth perception problems. The lady you saw that tipped her scooter at Epcot, I would bet 99.9999% was somehow in error. Like too much speed, too tight a turn, bumping into something, not remembering how to stop the machine. Again, these are car driver skills that also apply to scooter use.
I would not hesitate to recommend a 3-wheel scooter to a qualified rider at Walt Disney World. Much easier than a 4-wheeler to maneuver through stores, hotel rooms, restaurants, and tight ride lines.