I choose to recognize that I'm watching a film and TV franchise ...
I choose otherwise, when I watch Star Trek or any other show I want everything I see and hear to be "in universe." Not the producer/directors/writers did this or it only a TV show or those are just the FX of the day. What is on the screen is actual what is happening in the story.
Spock knows what Jim Kirk looked like when Kirk took command of the Enterprise because Spock was already aboard at the time. As a senior lieutenant (or lieutenant commander) he would have been one of the first people on board the Enterpise to meet Kirk. They were long time friends, Kirk wasn't just some guy he was meeting in a cave whos age he was guessing.
AYEL: "What is the current stardate? "
ROBAU: "Stardate? Twenty-two thirty-three zero four."
Now sure, the wise and powerful Robau could have meant "point zero four." He could have been using verbal shorthand. I can refer to the year as "oh nine" or "ninety-eight." But what we heard on screen was a six digit stardate. This is just one of the many clues that we're watch a non-TOS universe.
Remember, what JJ Abrams says in interviews and what the writers intended
isn't canon. What's on screen is.