Maybe Sarek adopted another human kid.
So if I had a brother that you had never met or even knew about, and my dad said to you, "My son just got married," you'd automatically assume it was me because you never met my brother?
But this is fiction not real life. When it comes to fiction, only what is showed or at least hinted in the text is canon so yeah, unless someone says that Sarek has another son beside Spock, said son doesn't exist. The writers have to create him.
Sarek isn't a real living being who can get out of his fictional reality and tell us 'you know, it is never showed but I actually have a son, 3 daughters, 2 dogs and four cats'.
The irony of your argument is that you are saying that in a thread where you are also adamant that Spock and Uhura couldn't possibly end up together in tos or be interested in each other just because they
didn't show them being a couple there (only some hints of attraction and tptb saying that it was the original plan), and yet you want to dispute Spock being the son Picard was referring to on the basis of you thinking that Sarek had another son in spite of never seeing him and never getting any hint of his existence.
I don't
think tos Spock and Uhura were together, but using your logic about Sarek's imaginary son never mentioned in canon, one could assume a lot of things happened to the characters that we just didn't see on screen.
And frankly, the idea
many fans had that Spock and Uhura were at least attracted to each other (including
Nichols herself) in tos too is less baseless than your 'Sarek has another son we never heard about' theory.
The idea of them being together or interested also isn't more baseless than spock/saavik or scotty/uhura (like, how? At least she actually flirted with Spock)
If you just dislike the idea of Spock falling in love (thus him possibly deciding to marry someone out of love), then it's another matter and a different opinion than you disputing whether or not he was the son of Sarek whose wedding Picard went to. Using your logic, it wouldn't matter anyway because even if he weren't that son, nothing says that Spock couldn't have found someone in prime trek too, eventually, and thus have a private life you just don't know about..