When applied to a person, usually to go blue is an idiom that is used for the couple of facial expressions where oxygenated blood drains from the face, leaving the pallor of the face blue; what comes to mind for me are the emotions of embarrassment, shock, and exhausted anger. If someone had told you in the middle of a birthday party your brother had died, at the ripe old age of 24 years, it wouldn't remiss for an observer to describe your face "as going blue" retelling the story of your receiving the news.
Some example sentences:
She went blue at the news that she was being fired from her job of 30+ years with no severance and 1 week notice.
You can stamp and yell and go blue in the face all you want, but you're not still getting an Illudium Q-36 Explosive Space Modulator for Christmas.
After spending $10,000 on an engagement ring, her boyfriend went blue at her unexpected rejection of his marriage proposal.
Unfortunately, the sources you link here seem to be using to go blue in a bizarre sense I have never seen before. I thought at the first the second source might correspond to this idiom, since a commenter there writes something like "nonsense...you went red", which is definitely an identifiable idiom for being embarrassed, but her reply comment seems to disagree with his interpretation. I wasn't about to watch the whole video and watch "close-ups" to gauge her blueness as she wanted, either.