The mistake in the article in the OP is the date, "1963-1964 Cyprus crisis".
The problem occurred in 1974 and did relate to a/the Cyprus crisis.
According to U.S. Nuclear Weapons in Europe at page 25:
A prolonged congressional debate and a series of internal Pentagon reviews in 1973 and
1974 led to a conclusion that there were an excessive number of nuclear weapons in
Europe as well. Secretary of Defense James Schlesinger directed the first major revision
of its nuclear posture in Europe since they were initially deployed in 1954.
Schlesinger’s views were partially influenced, according to one recent account, by the
outbreak of war in July 1974 between two nuclear-equipped NATO countries, Turkey
and Greece. Schlesinger wanted to know if the U.S. nuclear weapons were secure and
asked his director of telecommunications and command and control systems, Thomas C.
Reed, if he could talk to the U.S. officers holding the keys to the weapons. Reed reported
back that the U.S. custodians were in charge, but at one Air Force base “things got a little
dicier.”
“The local Army troops outside the fence wanted in. Their Air Force
countrymen inside wanted them kept out. The nukes on alert aircraft were
hastily returned to bunkers as the opposing commanders parleyed under a
white flag. Soon both sides went off to dinner, but through it all we held
out breath.” [cites to reference 39: Thomas C. Reed, At the Abyss: An Insider’s History of the Cold War (Ballantine Books, 2004), p. 173]
The document goes on to state:
As a result of the Turkish-Greek
war, the United States removed its nuclear bombs from Greek and Turkish alert fighterbombers
and transferred the nuclear warheads from Greek Nike Hercules missile units
(see Figure 9) in the field to storage. Greece saw this as another pro-Turkish move by
NATO and responded by withdrawing its forces from NATO’s military command
structure. This forced Washington to contemplate whether to remove its nuclear weapons
from Greece altogether, but in the end the Ford administration decided against it after the
State Department warned that removal would further alienate the Greek government from
NATO [reference 41]
Nothing was said about this nuclear dilemma in the final communiqué from NATO’s
Nuclear Planning Group (NPG) that met in December 1974. The group remarked it had
“discussed the recent legislation in the United States calling for an examination of the
doctrine for the tactical use of nuclear weapons and of NATO's nuclear posture….” [reference 42]
Other than that, the public was kept in the dark.
The Turkish and Greek episode and the discoveries at Pacific Command led to immediate
improvements in the command and control of the forward-deployed nuclear weapons. A
wave of terrorist attacks in Europe at the time added to the concerns. By the end of 1976,
all U.S. tactical nuclear weapons were equipped with Permission Action Links (PALs).
The June 1975 NPG meeting made a vague reference to this by stating that, “actions
[were taken] to enhance the security of nuclear weapons stored in NATO Europe.” [reference 43]