I have refrozen meat many times. With ground beef, if it has been properly refridgerated, there should be no problem. Beside, the critters that grow in the meat will be killed when the meat is cooked. Of course this means grey, all the way through. Ground beef, whether it's used in chili, soup, hamburgers, meatloaf, or however you're going to cook it must be brought to a temperature of 165 minimum, and with absolutely no pink showing.
This is because the micro-organizms that cause sickness is mixed throughout the meat by the grinding process. Unground meat contaminants are found only on the outer surface, and are destroyed when that surface is heated. And I don't know about you, but that surface is in contact with at least 325 heat no matter how I cook it, more so on the grill, or in a frying pan. So that means the surface is exposed to high heat, killing the little nasties. The middle can remain pink, or even red in steaks, and pink in pork. My poultry needs to be white throughout, unless we're talking smoke ring.
Seeeeeya; Goodweed of the North