The problematic bacteria that sometimes exist in beef products is typically only on the surface of the meat. This is why you can eat a steak rare (you kill the bacteria on the surfaces when you brown the steak).

If you buy ground meat, chances are that some of the bacteria from the surface of the meat is now mixed throughout the ground meat. This means that you have to cook it all the way through.

At a restaurant that is serving burgers that aren't cooked all the way through, they will (hopefully) have removed the outer surface of the meat before mincing the meat, which is why it is considered to be safe.