This is a fringe but real argument in American semantics.
As you note, "a social event featuring this type of cooking" is an acceptable use of BBQ, but NEITHER brats nor burgers are considered Barbecue by the majority of Americans. (Since they are not barbecued, but grilled. Calling them barbecue would be like calling a roast "braised", yes, it happened in the same cooking appliance, but it happened VERY differently)
As such, the event does NOT feature barbecue, and should not be CALLED a 'barbecue'. Such an event 'should' be called "a cook-out", "picnic", or something similar. However, informal usage of the term has created a large population that uses the term "Barbecue" to refer to any outdoor gathering centered on food.
And THAT irritates barbecue purists.
The distinction actually came up in a campaign speech by Obama at one point, where he pointed out that the event he was at was not serving barbecue, and therefore, in his neighborhood, would have been called a "cook-out", before diplomatically pointing out "but whatever you call it, it's a heck of a good time. "