What do you give your dog at a barbecue?

I'm of the "no people food" class of dog owner. However, I get the impression that the woman who fostered Rosie before we added her to our family wasn't so careful. She claimed that she only feeds dogs appropriate food but I noticed that she was awfully free with cheese for instance. Also, whenever we have had people over for a barbecue, Rosie (who is very shy around strangers and almost never begs for food) works the crowd like a pro. She has killed puppy dog eyes. I'm pretty sure her foster mom had lots of parties where the guests were "dropping" food all over the place.
So, to my original question, do
you think an occasional piece of hotdog or burger is such a bad thing? My husband and I barbecued tonight and as usual the dogs were hanging closely around the grill...