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It's not just time zones and leap seconds. SI seconds on Earth are slower because of relativity, so there are time standards for space stuff (TCB, TGC) that use faster SI seconds than UTC/Unix time. T2 - T1 = [God doesn't know and the Devil isn't telling.]
I got to "The day before Saturday is always Friday" and I was like waaaa?
I thought it is about when Julian calendar was dropped in favour of Gregorian, but that's not it:
Also some of the islands around the International Date Line did switch their stance on which side of the Date Line they are. So... they might have had a day twice or lost a whole day in the process. And maybe, they didn't change sides only once...
E.g. see here https://youtu.be/cpKuBlvef6A
A great video you linked, the missing Friday is in it on timestamp 22:45
The Thursday 29th of December 2011 was followed by Saturday 31st of December 2011 on Samoa