It's more flexible then that and this article specifically talks about that.
If it didn't take this position, it then makes nuclear war more likely. It is actually a logical position to take since you can assume tit for tat nuclear strikes are a given, so there is no advantage to drawing it out.
It may of course not take the option, but the opponent doesn't know what it will do. It's all a part of the nuclear force being a deterrent to war.
https://en.m.wikipedia.org/wiki/Mutual_assured_destruction
It requires only equal or greater response if the country is attacked.
It's completely within the doctrine to respond to a single nuke detonated by Putin on Ukrainian soil targetting Nato military forces, with a single Nato nuke, also on Ukrainian soil targetting Russian military forces.
It's a matter of policy that the US will launch all its nukes if even one nuke is launched by the other side. It only makes sense that the other side would do the same.
There is no such thing as limited nuclear war. If someone launches a nuke, all nukes are launched.
And that's why nukes work, they take war to its logical conclusion: everyone dies.
The US and Russia have enough nukes to destroy the entire world many times over. It doesn't matter where you are, you'll either die quickly or slowly, but you'll die none the less.