I looked it up and it seems that Disney requires cyclists to obey Florida's bicycle laws, which in turn requires cyclists to obey vehicle laws. This is no different than Georgia. The difference is we were on a trail or path shared by pedestrians. Florida does allow for this (I believe Georgia does too.)
The other difference was the path was full of pedestrians who had just gotten out of Hoop Dee Doo and off the Boat from MK. This family zoomed through the pedestrians, then stopped, got off their bikes for some reason, then got on again and zoomed through everyone again. Whether in Florida or Georgia, pedestrians have the right of way.
Either way, I was tired and wouldn't have been too upset, except the Disney traffic guy has rather short with me for walking along the golf cart path, which I switched to when we were buzzed by the cycling family a second time.
It's all good now. A brand-new day full of hope and opportunities.