Earlier quoted context omitted.
The best way to destroy an enemy nuclear weapon is by hitting it with one of your nuclear weapons. Add on top of that your other strategic targets and a reserve, and the fact that their calculation is the same as yours, and you can see where this is going.
With weapons distributed amongst all USSR holdings this implies the US was willing to nuke everything from Poland to north Vietnam.
In that context, you are already so resigned at killing others over your own safety, that hitting a few other countries is a no-brainer.