That's not true. As long as the meat has been stored properly and thawed slowly in the refrigerator, it can be refrozen safely multiple times. If done correctly, refreezing meat does not pose any health risks. Although, depending on the type of meat and how many times it's refrozen, the quality (taste/texture) of the meat could be negatively affected.
In other words, if you buy a frozen steak, sausages etc. thaw them in your refrigerator, then put them back in the freezer, they'll be completely safe to eat. Nothing bad is going to happen to it and that process won't make you sick. However, if you have meat that has microbes, bacteria, yeast, molds present, freezing will make them inactive, but once thawed, these microbes can once again become active and make you sick.
Simply thawing and and refreezing untainted meat won't cause it to go bad and become unsafe to eat.