Yes, for certain definitions of "trace amounts." If you order a vegan burger from a Burger King, you're going to get trace amounts of beef in your burger--from atmospheric contamination, if nothing else.

Personally, I'm with you that using the same grill is too much contamination, but it's a fine line. The only way to be sure is to have separate restaurants, which is what they do in Israel to keep kosher. They serve meat or cheese, not both, in any given restaurant.