I don't have Potbelly's specific recipe, but most "fat-free" vinagrette dressings rely heavily on corn syrup as a thickener and to dilute the vinegar. Given the sweetness you noticed with the Potbelly dressing, I would guess this to be the case with theirs as well. For example, these are the ingredients in WishBone's Fat Free Red Wine Vinagrette:
Water, High Fructose Corn Syrup, Red Wine Vinegar, Cabernet Sauvignon
Wine, Sugar, Salt, Soybean Oil (Adds An Insignificant Amout of Fat),
Garlic, Onion, Lemon Juice Concentrate, Xanthan Gum, Tocopheryl
Acetate (Vitamin E), Calcium Disodium Edta (Used to Protect Quality),
Natural Flavor, Sulfiting Agents.
Even "homemade" recipes involve large amounts of sugar: http://vegetarian.about.com/od/saladdressings/r/fatfreesalad1.htm
So in general you're looking for a recipe which involves corn syrup + vinegar + spices. Beyond that, online recipes abound.
Also, if you're looking for fat-free dressings for health reasons, you need to ask yourself if eating several ounces of corn syrup is really an improvement over a little olive oil.