I'm not sure why that's being dismissed. Standard advice for travelers to avoid thrombosis recommends leg exercises during extended sitting, including both toe and heel raises. "Shaking your legs" while sitting generally consists of either tapping your toes or bouncing your heels; heel raises in particular really are the same motion as fidgeting.

I wonder if standing desks can be just as dangerous as sitting if you are standing motionless for more than an hour or so.

I'd say it's much harder to stay perfectly motionless while standing than while sitting. Subtle shifts of weight from one leg to the other are enough to stave off DVT.