Were they allowed to take it back to share?

Yes, my reaction would have been to take it back to share with the camp. But if you look at the other prizes, they were all designed just for the two participants.

The treats seemed to be designed for the two individuals involved.
Take the fresh laundry, only two sets of clothes were there, the same with the ice-creams.
Chances are they wouldn't have been allowed to bring the pizza back to share.
Everyone had an equal chance of a treat anyway, hardly their fault.

I don't think they were allowed to bring their treats back to the camp to share.

I agree maybe they weren't allowed to take it back but it wasn't mentioned was it?

They weren't allowed to take their family back were they

I don't control the edit so I don't know. For all we know they may have been told before hand of certain rules, it may have been on the paper nailed to the tree or they may not have been told that at all.
I still don't see why people think they needed to share, they didn't know the others had nothing at that time. They may have assumed everyone had recieved some form of food, they only opened the one door afterall and weren't privy to what was behind the other doors aside from a game over sign behind one.
People on here do love to find fault though.

Yes, on reflection, I agree.

yes