I certainly think it is possible to have both. Heck, the BJCP style "Dry Stout" pretty much proves it. The body is defined as "Medium-light to medium-full," yet the name of the beer tells you it has to be dry. I think of dry as being devoid of sweetness, with a drying feeling in the mouth -- in this case, it comes from the high % roasted barley in the beer. In other products, as mentioned, high carbonation plays into it.
The increased body is often due to beta-glucans (gum/starch-like polysaccharides) introduced through the use of flaked barley. These contribute no sweetness, but give the beer its thick, creamy mouthfeel.