Everybody and their mother sent me this video as soon as it went viral, especially friends of mine that don't play Magic but are fascinated with my interest in the franchise.
Before I even watched the video for myself, simply reading about how a Black Lotus and Tropical Island were opened in the same starter made me raise an eyebrow. I knew that the pairing of the rares did not "make sense" with how the product was packaged back then.
Black Lotus was "always" packaged with Lord of the Pit, and Tropical Island was "always" packaged with Bayou. (The latter is true in Revised starter decks, as well.) Many high end collectors and enthusiasts of Magic's early history are aware of how certain rares were packaged together based on the layout of the original sheets.
Something crossed my mind during all of this: Volcanic Island. Volcanic Island was accidentally omitted from the "Alpha" print run. It was then corrected with the "Beta" printing of the set. If you look at an uncut sheet of Beta, though, you'll see that Volcanic Island is somewhere in the middle of the sheet, which is a bit strange, as it was the only rare that was accidentally left off. (Circle of Protection: Black also didn't see an Alpha printing.) It's extremely likely that the entire rare sheet was reorganized, but there's no way of knowing, as no uncut sheets of Alpha (knowingly) exist. If the sheets were reorganized for Beta's printing, then it would explain how rares could have been packaged together differently in Alpha starters when compared to Beta starters.
Here's a picture of an uncut sheet of Beta:

Let's look at a couple of things.
Cards that I highlighted in one yellow box represent cards that were visually documented as being opened together out of an Alpha, Beta, or Unlimited starter deck that
are contiguous on a sheet of Beta.
1.
Tropical Island and
Bayou (
Alpha starter)
2.
Deathlace and
Fork (
Beta starter)
3.
Time Walk and
Underground Sea (
Beta starter)
4.
Savannah and
Mox Ruby (
Unlimited starter)
5.
Ankh of Mishra and
Howling Mine (
Beta starter)
6.
Warp Artifact and
Granite Gargoyle (
Alpha starter)
7.
Deathlace and
Fork, again (
Alpha starter)
8.
Black Lotus and
Lord of the Pit (See below)
(There is no video documentation of a Black Lotus being opened alongside a Lord of the Pit, but there are stories and forum posts dating years back of people telling about how they opened up a Lord of the Pit and Black Lotus together. These were random people who likely had no reason to lie. It was also before the popularization of filming sealed product being opened. Even if people were lying, it's hard to imagine that people that would stoop to lying would accurately know about the ordering of rares... and if they wanted to make up a great story, wouldn't they have chosen the neighboring Mox Emerald instead of the Lord of the Pit?)
Cards that I highlighted in a color besides yellow are pairs of rares that were visually documented as being opened together out of an Alpha or Beta starter deck that are
not contiguous on the sheet.
1.
Winter Orb and
Mind Twist (
Beta starter)
2.
Braingeyser and
Tundra (
Alpha starter)
3.
Black Lotus and
Tropical Island (
Alpha starter)
4.
Dingus Egg and
Living Artifact (
Alpha starter)
5.
Taiga and
Fastbond (
Alpha starter)
For argument's sake, let's just assume the videos are real. I have an incredibly hard time imagining that the video in question (or any of them, for that matter) are faked, as the cards are all ridiculously crisp and consistent with one another in condition and printing similarities. This would be rather tricky to fake, especially since there's really no fantastic "gain" in fabricating something like this.
All of the rares that were opened together that weren't contiguous with each other are from Alpha starters, with the exception of Winter Orb and Mind Twist, which is noteworthy, as they are both conveniently on the corners of the sheet. I am of the assumption that Alpha's rare sheet was organized in a different fashion and then re-organized for Beta as misprinted cards were corrected (Cyclopean Tomb) and missing cards were added (Volcanic Island).
It's still incredibly interesting that two Tropical Islands have been opened out of Alpha starters featuring different companion cards (Black Lotus and Bayou). Also, Deathlace and Fork have been opened together in both Alpha
and Beta starter decks. I think it's somewhat safe to assume that the Alpha rare sheet was different than the Beta rare sheet, but not
completely different. I'd really like to learn more about this, if anybody else has some thoughts or information on the matter.