>>56229969>>56229730It doesn't have anything to do with fateful encounters or not.
I won't go to far into the spaghetti code that Pokemon games use. But what determines if something is shiny is the PID, the IVs and the nature (PV). A sub code that is part of the PID is called the "Xor value". And that code can have any value from 0 to 15. If a Pokemon has a PID with a Xor value of 0, it is a square shiny.
For example, here is shiny Celebi from the virtual console Crystal and it has a fateful encounter Xor 6. And also Diancie from a mystery gift Fateful encounter, with Xor 0.
Game Freak these days sets all Mystery Gift shinys to Xor 0. Why? Who knows.