In this article Putin responds to criticisms on the Ukraine and on human rights abuses in Chechnya where family members are punished even if they did not support the actions of militants (it doesn't say in the first article but it says in this one: http://itar-tass.com/en/russia/767808) by mentioning legalizing torture in the United States.
If there had been no torture or if all who had been involved in ordering torture were tried and convicted in a court of law we would have a much better moral leg to stand on.
It would also have been better if we hadn't invaded Iraq under Bush. Then it would be easier for Obama to do what we must do against ISIS (ignoring the fact for a moment that ISIS likely would not have even happened if we didn't invade Iraq) instead of having to worry about people who make a false equivocation between a full on war to stop ISIS and the earlier war in Iraq.
The United States has weakened itself on the world stage with torture and war based on faulty reasoning.
It's not that I think Putin would have backed down in Ukraine or respect human rights otherwise, but it would be harder for him to justify himself to his own people. Instead he can point to US actions to sell his "Westerners are trying to control us" narrative. It is just like how the Soviet Union deflected human rights criticisms by talking about racism and segregation in the United States.
The US can maintain its position abroad even without any moral high ground. Along with this the idea that the US is no longer on the moral high ground in quite false. The US is one of very few truly democratic nations In the world so a moral high ground is maintained.