When using priming sugar to carbonate beer it adds approximately .5% ABV to that beer. The additional alcohol, in theory, thins the beer.
One thing I would point out is that this "theory" is false. Replacing barley or malt with sugar will lower the body and malt character of a beer. Just adding sugar to a beer will boost the alcohol and alcohol adds a bit of body and sweetness to a beer (exactly how sweet alcohol tastes seems to vary from people to people).