Not So Fast, Comrades

When Alexander Litvinenko died, I turned in Putin's direction like everyone else, but a tiny little something's-not-right flickered in the back of my mind, not coalescing into a thought, when I read he'd converted to Islam on his deathbed. Then yesterday I heard a snippet of the guest-host for a 2nd or 3rd tier radio show saying that Scotland Yard is looking in a different direction now, because Litvinenko's body had a $10 million dollar dose of polonium 210, and if the KGB or CIA wanted to kill you, they could do it for considerably less. And now Pat Buchanan's on the case.
What benefit could Putin conceivably realize from the London killing of an enemy of his regime, who had just become a British citizen? Why would the Russian president, at the peak of his popularity, with his regime awash in oil revenue and himself playing a strong hand in world politics, risk a breach with every Western nation by ordering the public murder of a man who was more of a nuisance than a threat to his regime?
A quick google search reveals many people are also looking in the direction of Islam and away from Putin. Well, I don't know what to think. But Pat was right about John Djmanjuk (or however you spell it) not being Ivan the Terrible. Hmmm.