Also from the wikipedia article on “barbecue”
In American English usage, grilling refers to a fast process over high heat while barbecuing refers to a slow process using indirect heat or hot smoke, similar to some forms of roasting. In a typical U.S. home grill, food is cooked on a grate directly over hot charcoal, while in a U.S. barbecue the coals are dispersed to the sides or at a significant distance from the grate. In British usage, barbecuing refers to a fast cooking process done directly over high heat, while grilling refers to cooking under a source of direct, moderate-to-high heat—known in the United States as broiling .
My point is that even among English speakers, as is often the case, the term is used to mean different things, and the sources you cite to declare a specific meaning do not in fact support your claim.
