From what I’ve gathered, 1/16,384 isn’t quite correct, but isn’t quite false, either. I’m not a dataminer, so I’m relying off of what others have said (such as in the videos you’ve linked), and it sounds to me like the game generates one shiny value every 4 days that it uses for each Pokémon during that time. If you use the time skipping method, but only skip one day at a time, then you’re only seeing Pokémon with a new shiny chance once every four days, effectively quadrupling (or quartering?) your odds. This is why some sources will tell you that you need to skip ahead four days for each encounter. This four day system that the game uses only really affects time skipping, though, since it still uses the standard 1/4096 odds for each four-day block. You could also go between two nearby dens, use a wishing piece, check if its shiny, reset after seeing it, then go to the other den and repeat. This will give you the standard 1/4096 odds, since each use of a wishing piece will generate a new seed.
So in summary:
Time skipping one day at a time: 1/16,384
Time skipping four days at a time: 1/4096
Spamming wishing pieces on dens: 1/4096