You are right about the wheels. When a big cycling charity ride — thousands of people — crosses railroad tracks at an angle, there are always multiple people who catch a wheel in the tracks and take a spill. For bike wheels you need that special condition of a narrow groove the right size, but for the tiny wheels on the older scooters, it's much easier for almost any angled imperfection in the pavement to grab your wheel or simply knock you off balance if you don't take care to hit it right. Anecdotally, it's something you have to be constantly aware of on imperfect city streets, and I took a bad spill when I hit something on the street that I didn't see in the dark.

That said... the biggest danger is always collisions with cars, which is the same danger you face on a bike, and the danger the article concentrates on. I almost got hit on my bike by a car turning right across the bike lane just yesterday, and the outcome was a matter of luck, not a matter of what vehicle I was on. The article mentions the "Three E’s of Traffic Safety: engineering, enforcement, and education" and I think we need more of all three. The driver who almost hit me (I caught up to him and spoke to him) was an older man who looked to be from out of town and probably had no idea he needed to check his blind spot when turning right, because that simply wasn't a thing until the advent of bike lanes, not when he was learning to drive and maybe still not in the town or city where he lives.

EDIT: You're also right about braking. The wheels skid easier than bike wheels, and it's harder to keep your weight back and down so the braking force gets transferred to your body.