They’re taking about a white sauce for chicken and when most people around the South think about barbecue sauce they mean a tomato or vinegar based sauce for barbecued pork.
Sounds like you grew up on that Ollie’s vinegar based sauce.
Yes, Ollie’s was my Dads favorite and he also spent years trying to duplicate the recipe.
I ate at Ollie’s a few times. A really good sauce. I think you can still buy it at the grocery, some places