Depends on how badly it is broken. I'm not a doc so I am not going to give you advice based on your x-ray (although I do have an opinion). They seem to talk about displacement (how far the bone is out of alignment) and the length of the break itself. My break was the long way across the bone and the displacement was huge, so pretty much everyone who looked at it said surgery without batting an eye.
I'd actually be curious to hear your opinion...obviously you're not a doctor so my doctor's opinion would trump yours :-). I say this because from the wise and all knowing Interweb, 90% of clavicle breaks don't require surgery. If yours was one of those, how much farther apart (if at all) were your bones than mine?