Both Politkovskaya and Litvenenko (of "death by polonium poisoning administered in London" fame) are most notorious for promoting the theory that the Russian FSB in general and Putin particularly were responsible for a series of apartment bombings in Russia that killed hundreds of people and formed the casus belli for the Chechen War.

So, attributing their death to "Chechnya" is a little like attributing a hypothetical murder of Sy Hersh to the Iraqis.

Shorter: no, I think you're wrong about this.