Welcome to the forums.
Actually, a CCT is just a number. It is not a point on the x-y plane, on the Planckian locus or otherwise.
But if you "ask for" the chromaticity whose CT (not CCT) is that CCT value, then you have a particular point on the Planckian locus (and thus a specific chromaticity).
If you ask for "something" whose CCT is that value, you get an iso-temperature line.
With all due respect, but do you really think that this nitty-gritty word-game is a useful contribution to the discussion? I believe that Serge's conclusion clearly shows his understanding of the concepts and the corresponding ambiguities.
And again, you are also reversing the logic:
[geek warning on]
If you have a chromaticity of a selective radiator that is not equal to any of the chromaticities of the blackbody radiator, then the CCT is defined as the temperature of the blackbody radiator whose perceived color most closely resembles the perceived color of the selective radiator.
This is almost verbatim from Wyszecki & Stiles, which I presume is still the reference for this subject.
[geek warning off]
In normal language: if you have a color close to the planckian locus, then the CCT is the closest color ON the planckian locus. PERIOD.
Obviously, no software (or scientist) is going to ask for a CCT as opposed to a CT, and then pick a random color on the iso-temperature line. Although given the wildly varying results of current software offerings, one would be inclined to think they actually do pick a random number... (joke).