I also recalled hearing exactly this. In fact, in my recollection Burger King had a vegetarian burger option for some time before dropping it due to complaints of it being prepared on the same grill as the meat patties. Meanwhile McDonald's also offers vegetarian options which apparently aren't prepared separately to avoid cross-contamination. Only their options seem to vary quite a bit by region, so maybe they've just cleverly avoided the scrutiny that comes with a global marketing offensive like this.