Putin used to be KGB and rose up through the FSB. He has cemented his hold on power through plausible deniability. The FSB or other parts of the Russian government never get their hands dirty with poisoning people or assassinations. Instead, people who want something from the government (contracts, loan forgiveness, etc.) will approach a government official and tell them that they know the government isn't happy with (insert journalist, opposition leader, oligarch, etc.). The government official then lets that person know that they know that they want the contract for the new water plant and appreciate their concern about (journalist, opposition leader, etc.). This is a signal that the government will do what you want if you take out their enemy. These communications can often go through multiple intermediaries to maintain plausible deniability or to just cover tracks completely.
Putin definitely understands that the oligarchs are the only check on his power. It seems pretty clear that Putin is doing everything he can to make sure he consolidates power among his closest and most loyal oligarch allies and is trying to take out anyone who might be a threat to his hold on power.