This is NOT photoshopped, it is completely, 100% VALID.
I found your BBS doing a google search for the clip of Spock on Carol Burnett. I'm an old lady who remembers TOS from when it originally aired in 1967, and I was a huge fan of Carol Burnett. I remember actually seeing the episode on Carol Burnett, and the sketch where she had married the Invisible Man. I nearly DIED from laughter when Mister Spock walked through the door, and the reaction of Carol Burnett was priceless. I doubt she even knew that somehow they found Spock in full Trek regalia to appear.
Yes, it is true, Carol Burnett was on CBS, and Star Trek was an NBC show. I never saw an explanation for this ANYWHERE, and that makes me think it was entirely unsanctioned. I have never seen a rerun, either.
But take it from an old lady who KNOWS. It actually happened!
(edited to add: it had nothing whatsoever to do with Dr Spock)
I can't find any reference to Star Trek
and The Carol Burnett Show
having a common studio or corporate ownership either, but Wikipedia lists Leonard Nimoy as a Season 1 (1967) guest on her show.
To appear as Spock, Nimoy must have had the consent of William Ware Theiss for the costume. Also, make-up man Fred Phillips must have accompanied Nimoy to Carol Burnett
to get his ears and eyebrows on.
And I'd say Carol Burnett had
to know he was appearing, because you can't sit in her make-up department for two hours becoming a Vulcan without her noticing.