Could it be that crop sensor manufacturers just "advertise" their lenses at F1.8, F2.8 or whatever equivalencies just to marketing purposes? And that this doesn't apply to Medium format. I don't see any other reason for it to be that way. So in reality an F1.8 ASP-C lens is an F2.7 lens and they are just marketing "equivalencies". I don't even know how they are applying F-stop in this case to the crop sensor.
They do not.
5.6 is always 5.6, and gives the same exposure regardless of type of lens, focal length, or format. The clue to this is the term you used: crop sensor. Put a full-frame Nikon lens on a crop sensor Nikon camera, and the only difference is that the whole image will be smaller than it is on full-frame, but any object in the image will be the same size. All that has happened is that the full-frame image has been cropped. No change in exposure. At the same ISO and shutter speed, a full frame lens and a crop sensor lens will give the same exposure at the same f-stop. Put a crop sensor lens on a full-frame body, and at a given f-stop, the exposure will be the same as with a full-frame lens. The difference will only be that the crop sensor lens will not cover the full frame.
A given f-stop on smaller and larger format lenses always produces the same exposure under the same conditions, if the shutter speed and ISO number do not change.
For example: Pentax made cameras in 35mm format, 6X4.5cm format, and 6X7cm format. For each of those formats, they made a 200mm f/4 lens. The lenses have the same focal length and aperture number. The 645 format lens is physically larger than the 35mm format lens, and the 6X7 lens is larger than the 645, but the maximum aperture of each lens is physically the same. And the diaphragm opening at say, f/8, is physically the same in all three lenses. The difference between them is that they create different size image circles, depending on the format they cover.
Pentax made adapters for the 645 and 6X7 lenses so they could be adapted to a smaller format. Pentax 645 lenses could be adapted to Pentax 35mm cameras, and Pentax 6X7 lenses could be adapted to both Pentax 645 and Pentax 35mm cameras.
All three formats' 200mm f/4 lenses, on a 35mm camera, give the same image on the 35mm frame. At a given f-stop, all three give the same exposure and depth of field. All the 35mm camera did was crop the larger format lenses' larger image circles more than its own lens's image circle.
All three 200mm f/4 lenses are telephotos in their respective formats, making this example straightforward. But on the larger formats, 200mm is less of a telephoto. On 6X7 it is equivalent to 100 mm on 35mm format. Its optical design gives it a wider angle of view, and it is that wider view that fills out the larger format to its edges. A 50mm lens for 35mm format has a "normal lens" optical design, as does a 100mm lens for 6X7. But on 6X7, a 50mm is a wide angle lens, and has a wide angle design. Still, adapted to a 35mm camera, it will give an image the same size as the 50mm lens for 35mm format, and the same exposure for a given f/stop.