The issue with the meat thawing is the temperature of the meat going into the "holding" temp range. That is when the bacteria that is in the meat will grow quickly. Some bacteria are killed by low and high temps, and some absolutely thrive in cold temps - eg listeria.

When cooking food, you want it to get to 75C and if you are reheating, to 60C as quickly as possible.

in your case.. the freezer would have had to get above 5C and stay above that temp for a min of 2hrs for you to be concerned about the meat.

You are perfectly safe to refreeze it. Being a deep freeze it would be around -18C and would take a while to heat up to 5C. You only loose quality in the meat if it is completely defrosted, then re-frozen.. it dries out.

hope this helps..

food standards australia is a great source to what is acceptable in kitchens.