Did they use it on a 75 year old guy with AIDS?
As far as I know, Russia is the only power which has used polonium as a weapon. Which brings up the question, why would Russia have wanted to do in Arafat?
Then again, maybe Mossad did do it, hoping for the small bonus of having their achievement pinned on the Russians. However, that doesn't fit the chronology: Arafat died in 2004, but Litvinenko's assassination took place late in 2006 and is the first known case, I believe, of polonium's use as a weapon.
They didn't identify polonium as the cause of Litvinenko's illness until a few days before he died. However, once they did, Scotland Yard found traces all around London where Litvinenko and his assassins had been, and the trail led across Europe to Germany and and pointed east to the Former Evil Empire.
Most likely theory: the wogs are hoping to rebut the theory Arafat died of AIDS.