This is both true and false. It all depends on what you’re grilling, how you’re grilling it, and with which ingredients.
For instance, a Portobello mushroom can count as free OR as a fat if using oil.
It can also count differently depending on if you’re laying it right on the grill, allowing fat to drip off, or if you’re putting it in foil onto the grill to cook in the fat.
When it comes to grilling, you really don’t need oil in most cases. Stick to spray oils when needed, and cook directly on the grill to avoid the added calories and fat.