I biked as my only method of transportation in Boston and New York for years, and never did I have to dodge a projectile coming from above, parachute or otherwise.
I didn't say cyclists constantly dodge projectiles-- I said fast=moving obstacles, like cars and car doors. Having dodged quite a few car doors in Boston myself, I have a hard time picturing someone who could do that being dangerously thrown off by a little key floating down on a little parachute.