Wishmaker Jirachi fateful encounter or not?

[stringDTD]

According to Bulbapedia and this video showing how to get (shiny) Jirachi from the bonus disc (6:13 in video), it shows as fateful encounter; however, on PKHeX event data base, it does not have the fateful encounter box checked and shows as legal. If I manually tick the fateful encounter box, it shows up as illegal. Just want to know what this means, does the fateful encounter check gets removed from cross generational transfer or am I missing something?

[Kaphotics]

Fateful Encounter was a met location in gen 3. The obedience flag is what turned into the Fateful Encounter flag in future generations.

[stringDTD]

1 minute ago, Kaphotics said:

Fateful Encounter was a met location in gen 3. The obedience flag is what turned into the Fateful Encounter flag in future generations.

I remember hearing something like that before. Just to be clear, fateful encounter check only exists as its own obedience checker in gen 3 and it gets removed in later gens? Like are there different checks for obedience fateful encounter vs normal fateful encounter? Because I think I heard that Japanese faraway island is also a fateful encounter; however, it still shows up as fateful encounter in later generations. Sorry if this is just a newb question, I'm just confused on how it all works.

[theSLAYER]

Fateful encounter location in gen 3 does not transform into fateful encounter on later gens.
Obedience flag in gen 3 becomes fateful encounter flag in later gens.

For simplicity sake, PKHeX simply called Obedience Flag the Fateful Encounter Flag.

Jirachi does not have not have it.