This isn't true in my experience. I have ridden through areas like this often, because for some reason my city put one of the main bicycle routes through a busy pedestrian tourist area, full of families and inebriated diners.

If you dismount and push a bike, people get struck by pedals and handlebars. The rider has to allow much more space to prevent people walking right into them.

Riding at walking speed, some pedestrians may give a bit of space, but most of them don't alter their movement in any appreciable way. A capable rider has better control of a bicycle when they are actually riding it, and can keep pedals away from shins even in close proximity.