I agree about the definition, except for the "over a fire" part. I think a "fire" and "over the fire" are optional, but definitely the meat needs to be caressed with wood smoke. The location of the heat source, and whether or not it produces a fire is not relevant so long as it is cooked properly and smoked.
Not all will agree on all points with everyone though.
As for whether it insults me when people use the word for something otherwise...
It doesn't bother me one bit. Why the fark would I let something so trivial get me so upset when it makes no difference to anything, really?
Now, if some neighbor starts letting their dog crap in my yard, maybe that would bother me a bit. But not someone calling something they took off a grill or out of a crock-pot "BBQ". Then again, some people jsut like to bitch about anything and everything.