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Forget about the surface texture; if the belt was moving relative to the air, there would still be a no-slip condition between the flow and the belt surface, which is why a boundary layer forms in the first place.
The airspeed and belt speed are the same; there is no acceleration of air by the belt, and no boundary layer forms between the belt and flow. This is what happens to a car on the road; to accurately represent that, you must have one boundary layer under the car, between the car underbody and the airflow. A second boundary layer between the ground and flow results in a u-shaped velocity gradient.
Elevating a car in a wind tunnel is a common practice for correcting for both wheel drag when using stationary wheels and floor boundary layer when using a fixed floor.
I'm travelling right now, but when I get home next week I can post the relevant pages from some textbooks, including Hucho's Aerodynamics of Road Vehicles, that might explain better.
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