Well as a fellow Miata owner (NB second-gen), I know that the first (NA) & second-generation body styles had a vinyl cover that was secured with snaps on the interior of the car. I never used my vinyl cover because frankly it was a waste of time to put on. I just wanted to drop the top and go!
The tops of the first two generations of Miata would just fold back and expose it's top latch to the air. This made it look not as flat and clean-looking.
The current, third generation uses the Z-style folding top which folds more flatly onto itself and is more clean-looking. I'm not sure if the new Miata has a vinyl top cover or not, but it probably wouldn't need it anyway due to the Z-folding top design.
So back to your question...yes the Miata has a cover for the top, but no, I don't know anyone who would ever use it which is why you saw the Miata without it's cover.
"Look! Up in the SKY!"
Mods: RK Sport front valance, Fujita intake, Magnaflow exhaust, black 19" J2's w/ Falken FK-452's, yellow calipers, Opel badging, stubby, 6000k HID's, 15% tint