Funny that you say so, given that I have never pointed it out to you before.
That is correct. The US proposed "universal" (which practically at that point just meant the US) nuclear disarmament with inspections. That was the Baruch Plan. The
Baruch Plan proposed:
1. extend between all countries the exchange of basic scientific information for peaceful ends;
2. implement control of nuclear power to the extent necessary to ensure its use only for peaceful purposes;
3. eliminate from national armaments atomic weapons and all other major weapons adaptable to mass destruction; and
4. establish effective safeguards by way of inspection and other means to protect complying States against the hazards of violations and evasions
The Soviet Union rejected that proposal, and instead proposed "universal" nuclear disarmament
without inspections.
IOW, the Soviets wanted the US to give up
its' nukes, but were unwilling to sign on to any regime which might keep
them from then developing nukes.