The potential for contamination is on the outside of the meat. The insides are sterile. If you get a steak or other chuck of beef and clean it, you don't have a problem. Thus you can slice and eat. Or, cook the outside to high temps and leave the inside either cold or barely warm and, still, no problem. You could even hand grind it and have no problem. The BIG problem is when you have a large industrial operation and you don't meticulously clean the chunks of beef before you grind. None of those operations can, without fail, clean all that meat and quite a few use "beef recovery methods" that are best left to another post. Given that mutant e. coli contamination is rare (let's say one in a thousand), then there's very little risk in taking a chuck of beef and grinding it. However, if you routinely take thousands of chunks of beef and grind them all together, or at least with the same equipment, - like the major processors do - then you have a significant chance of contamination to all of your product. As much as I LOVE rare hamburgers, I really don't want one from a restaurant where they buy from one or more of the mega producers. Only your small place, where they can grind their own, can safely serve rare burgers. The best solution is buy and clean your own beef and grind or chop it yourself and grill to your personal specs.