I never had to have the key in the ignition of my 11 SE Hatchback in order to turn the steering wheel. I have pushed it around my shop with no key in it, or even a battery! Have you confirmed that the steering wheel actually locks when the key is out?
I always have used the magnetic mount trailer lights if my dollie lights were acting up. My Demco car caddy has steering linkage. Any car i was towing would require me to unlock the steering to have the dollie turn. I have never had to do anything with the Fiesta in regards to having the key in the ignition and such. It's never locked. So, in that regard flat towing and using a dollie with a steering linkage design, are similar.