Yes, that is surely correct.
But it really does not frighten me.
Putin is, I believe, a rational person; so I simply cannot imagine that he might use strategic nuclear weapons against the US. (I heard on the news, just the other day, that Britain has enough nuclear weapons to totally destroy all of Russia. And we have more nukes than Britain does. Yes, Russia has far more nukes than the US and Britain combined; but at some point, we are just talking about bouncing the rubble.)