This is such a silly aspect of this to be spending this many words on.

citation /sī-tā′shən/
noun

1. The act of citing.
2. A quotation of or explicit reference to a source for substantiation, as in a scholarly paper.
3. A reference to a previous court decision or other authority for a point of law, usually by case title and other information.

The American Heritage® Dictionary of the English Language, 5th Edition • More at Wordnik

This is number 2. Usually an explicit reference is enough, but in this case it's got the exact quote, the exact source who said it (you can contact him on Twitter if you want to verify it or find out more), why the source considered it reliable information, and why they should arguably be considered an authoritative source. Again: Doesn't mean what's in the video is true. But it forms a basis for starting to talk about whether it's true.

I think people have gotten accustomed to invoking the word "citation" as a way of disagreeing with something they don't think is proven, so much so that they've lost sight of the actual concept involved and the next steps once you have the source and what they said. It seems like at this point it's just a way to sound smart or skeptical in a comment.