The Tentcot has a set of tensioning straps on either end that connect underneath to the legs. They keep the assembly nice and taut. I don't see any reason you can't attach the end-straps to something else on your vehicle, perhaps. For example, I loop mine through the rails on my truck, and it keeps it from tipping, like so:
http://www.flickr.com/photos/17876474@N00/3413092343/in/set-72157616790168844/
http://www.flickr.com/photos/39730222@N08/3645131084/in/set-72157620706732745/
However, if you don't fold out the legs, it sort of defeats the purpose. Now you'd be lying on top of the folded legs across your butt, padded by only the 1/2" high density foam bottom. What makes the Tentcot so comfortable is that you are suspended like on a beach chair. I suppose you could somehow shorten the legs or something, but I think having the legs actually gives you more options for fastening to your roof rack, or whatever.
Also, I use the space underneath my Tentcot to throw my dirty boots when I get in, and my boots will be dry in case it rains.
Here are some pictures of a Landrover with a Tentcot on the roof (scroll to bottom of page):
http://www.rangerovers.net/outfitting/racks/classic.html
(Notice how he also loops the straps through his rack)