It was his claim. I heard it from him directly during his NPR interview on KQED.
The nonsensical part is that anyone pays any attention to him.
The whole anti-[something]ism thing is itself a problem.
Recently, we have anti-fascism and anti-racism. They both work on the same principle as McCarthy's anti-communism:
Declare yourself to be against something bad. Then accuse others of that thing you are against. Ruin their careers if possible. If anyone tries to stop you, accuse them of whatever it is you oppose.
Some of Joe McCarthy's targets actually were communists working in the State Department, but when he sad "I have here in my hand a list of two hundred and five people that were known to the Secretary of State as being members of the Communist Party and who nevertheless are still working and shaping the policy of the State Department", he was lying.