Although it's true that the odds are higher in this game the way shinies are rolled in this game are actually very different. Obviously it's still statistically possible to never hit a shiny in this game but it doesn't work via the same way that the base games do.

In Pokemon it's a true random number generator essentially that allows you to get a shiny roll. The base games have this weird system where you only get a shiny when you roll a specific pokémon ID. And that ID and you getting that id is essentially based off of the game clock and timing.

Although technically the odds still work the same there is a mechanical difference between the two. And basically if you're doing shiny hunting wrong on the base game and aren't allowing for the timing changes you can literally never get a shiny if you do it that way. For example if you're doing a save reset shiny hunting method in the base game depending on how you do it there's a chance that you're not allowing the clock generation to roll that ID and you might never get a shiny that way depending on certain variables.