OK, I can understand that's not the point you were making. I thought you were saying that because at many fast food places they
are literally cooking them in animal grease.
Many fast food places (McDonald's, Wendy's) use a flat surface similar to this:
https://upload.wikimedia.org/wikipedia/commons/c/cc/Flickr_X...
Typical ground beef is 20% fat (80% lean), and if you cook it on that, the fat will melt, it will hang around on that surface, and whatever else you cook next will be cooked in animal grease left over from the beef patty.
If you flame broil, the burger sits on a wire mesh, and the grease drips away.
I'm not just picking nits. I'm really trying to make a sincere point that I think one method will have significantly less transfer (not zero) than the other.