Refreezing foods is as much as a textural issue as a safety issue.
The rule about not refreezing has to do with the meat's cells breaking down due to the formation and re-formation of ice crystals and making the meat 'mushy'. With ground beef, that's not a serious issue.
On the safety side, if the meat was never exposed to temperatures warmer than the inside of the fridge, there should not be an issue. The exception being if it was kept thawed for longer that it's expiration date.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan