My two cents on this topic. Ground beef is more dangerous than steaks because it's all mixed together. ON a steak, harmful pathogens only exist on the outside, but in ground beef it's all mixed in. Now think of your typical home cook or barbecue situation. You defrost these burgers how? Leaving them on the counter? Maybe in a crappy cooler outside where you're grilling them? Maybe even grilling them by the dozen where they will sit at room temperature until someone takes it. Keeping meat below or over that danger-zone often does not kill bacteria, but keeps them from multiplying. Free to begin again as soon as you re-enter that danger zone.
Now if you've defrosted these burgers properly in the refrigerator (no matter how long your gigantic block of frozen meat takes.) and then taking them straight from refrigerator straight to heat, and finally right to someone's mouth, then cook them however you want! Otherwise, you're playing a dangerous game with ground, often inferior quality meat.
That said, there's nothing dangerous about ground beef cooked medium. As far as the pathogens that tend to exist in beef are concerned, well done is way overkill