NC has 2 primary style of bbq sauces, eastern-style and Lexington-style (sometimes called western-style). They are very similar; the primary difference being that Lexington-style has some kerchup in it. Here is the recipe used by the world famous Lexington #1 restaurant in Lexington, NC:
1 gallon water
1 qt. ketchup
1 qt. vinegar (amber 4% acidity)
10 oz sugar
8 oz salt
4 oz black pepper
4 oz crushed red pepper
Pinch of ground red pepper (cayenne)
Preparation: "Combine all ingredients into a 1.5 gallon stock pot and bring to a boil, stirring occasionally. Spoon the piping hot dip onto the prepared meat just prior to serving. This is a very thin sauce, but it is the same formula that has been used around here for generations." Allen Hege, Lexington Barbecue #1
The sauce you refer to is an "Eastern North Carolina" vinegar/pepper sauce. It is thin because the liquid ingredient is 100% vinegar (sometimes with a bit of water). Nearly every recipe will start with apple cider vinegar. Every person who makes a v/p sauce will have a different recipe. You can change it as you wish. The attributes of an authentic Eastern NC v/p sauce are acid, pepper, and salt. The sauce is obviously tart, and it will be spicy...unlike many of the bbq sauces you experience in other parts of the country. This v/p sauce will also be a tad on the salty side as it is actually used for seasoning the bbq. Many people don't like this style sauce and I always hear the complaint of, "it's too tart and it ruined my bbq." The main problem is most folks are used to thick bbq sauces that sit on top of the meat. You can also "see" a thick sauce sitting on the meat and know how much you've got on there. With a vinegar based sauce you have to use it as a seasoning and not a condiment. Nearly every person who complains they don't like a v/p sauce feel that way because they used too much of it. Used sparingly it is a fine compliment to pork bbq.
Some people use sugar...actually, alot of people use sugar in their Eastern NC sauce. My grandfather (who's recipe I use alot) forbids sugar to enter into his sauce. He uses nothing but pepper and salt. It's REALLY hot...just the way he likes it. You can, however, balance a little of the tartness and pepper heat with a bit of sugar. Don't make it sweet...just balance it out a bit.
A good basic recipe is:
1/2 gallon White House apple cider vinegar
1/4 cup crushed red pepper flakes
1/4 cup salt
2 Tbsp. white sugar
Add all the ingredients into, preferably, a non-reactive pot and bring to a good steam. You don't have to bring it to a boil. If it does come to a boil, it's ok...just remove it from the heat and let it cool. The pepper flakes will float. Once they start to steep in the hot vinegar they will sink. When the pot is steaming hot just turn the heat off and let it sit until cool. Then just pour it back into the container the vinegar came in (be sure to stir as you're putting it into the container as you want to keep the pepper in suspension). You don't have to heat the mixture at all if you don't want to. You can simply mix all the ingredients and put into a container. It's best to let the unheated sauce sit for 2-4 weeks before use to allow it to steep on it's own. Heating simply speeds up the process.
Now, you can change amounts and add ingredients if you like. To make it hotter, or more interesting, you can add additional pepper types...such as black pepper, cayenne pepper, or liquid pepper sauce. You can also lower the acid level by adding in some water. Adding in 1/2 as much water as vinegar will thin it nicely although I know some folks to add equal parts of water as vinegar (that's a little pantywaist to me as it takes away nearly all the vinegar flavor).
Good luck. A v/p sauce is really easy to make, and the combination of ingredients are endless. Try it and make it just the way you like.
Here's a hint...buy the 1/2 gallon container of a/c vinegar and only use half of it for your first batch. Cut the ingredients I listed above in half and try the sauce out. If you then want to adjust or add seasonings, make another batch with the second half of your vinegar. It's cheap to experiment! Good luck!!!
My family's sauce is very similar, except that we usually add a tiny squirt of ketchup - and I do mean tiny. I'd say less than a spoonful for a big batch of sauce. My grandmother was also known to toss a little worchestershire sauce in there (or, as she called it, "wooster" sauce) when she didn't think anyone was looking.