I had a hard time believing it either, so I tested it a couple of times.
without a doubt, if I take off the cap, my mpg drops considerably.
I bought my wife a moped a few yrs ago in Ft lauderdale, and of course I had to take my tonneu off to pick it up. and it took between 1/2 and 3/4's a tank just to get there, but we're talking about 1/3 less distance than MIA.
then another time I picked up a friend who came into the lauderdale airport, with the tonneu on I made the entire trip on 1 tank of gas. lauderdale airport is about 1/3 closer than miami's.