The only alteration the game does when generating the pokemon, in comparison to how it normally does, is that it skips the normal PID generating process and uses a fixed value based on the nature it wants.
The Smogon article is poorly worded -- you can't get every single option that was listed in that sentence, only those that are in the same "shiny group". You can get a few, but not every nature all in the same save file.
Pick a group, then get a TID/SID that pairs with that group to make it shiny, then use a searching tool like RNG Reporter / Pokefinder to see what IV spreads you can get shinies with.