Yes! It's a *very* unintuitive narrative, but it's a very real one that exists!
It makes zero sense UNLESS you look at the CIA vs FBI intelligence war in the 1970s and how that was a reflection of internal left vs right conflicts inside the military-intelligence establishment.
The CIA were the *left* edge of the military spook world. So they were seen by the conservative factions as Commies trying to subvert the system from within.