In this case, the "ounce of truth" is probably the legendary tale of how "Cap'n Crunch" and some friends managed to phreak their way onto a
private line in Nixon's White House. The Crunchman claims that they were listening to the line, and overheard the codeword to summon Nixon
("Olympus"). After, they got on the line themselves, asked for Olympus and someone who the Cap'n thought sounded exactly like Nixon came on the
line. Apparently one of his friends told Nixon that there was a crisis - a toilet paper shortage in LA.
My guess is that this story heavily inspired the one referenced in the OP. Possibly some other phreaking exploits got mixed in there as well. A lot of
interesting stuff happened in the heyday of phone phreaking.
From the horse's mouth: