When they go down, they would bring USA along with them, you seem not understanding their nuclear policy, when they got nuclearly attacked by other, no matter who is, they will launch their nuclear warheads against all other nations.
We had 100-200 nukes back then, if we launched all of these, more than half of USSR would turn into the stone age, sure that would force them to destroy the entire world.
That's why USA ultimately involved into this issue, because they didn't want to die together along with USSR and China.