no, it was always the other way around

Yes, but you said "Anouma said he took inspiration in western games for Breath of the Wild? "

And he clerly never said that.

While it's true that he never outright said it like that, his poor wording on his original comment of Skyrim completely give the impression of him being inspired by it, which is why he later had to clarify about his comments:

“Skyrim! Obviously I play other games, and I’m curious what Zelda fans like about the Skyrim experience. Maybe there are some Zelda fans who are looking for something similar out of a Zelda game. But I don’t look at the technology that made these games possible. I don’t look at what’s happening in the game, but how it made me feel, what in the game moved me, and how I can bring out those same emotions in players who play my games.

My intent isn’t to copy them, but those are the things that stay with you as a player. It’s not what you see but how the game makes you feel that makes you feel closer to the experience. It’s more about the feeling and expression of emotions in the game, and I do take that into consideration when working on my own projects. It’s like the difference between someone who takes a picture and looks at that picture when drawing a painting, and someone who sees something, keeps it in their head and then tries to recreate that."

He also admits, while dismissing that he's inspired from Skyrim, that influences might come from playing it (and others), as a natural process.

Breath of the Wild feels like a mix of a whole lot of stuff. The original Legend of Zelda is there but so are the items/abilities and puzzle-solving of the 3D entries. Then there's survival elements such as resource gathering, crafting and cooking, along with a dose of sandboxy "just goof around" stuff. There's also influences from games such as Skyrim and I'd say Xenoblade Chronicles as well.

Ugh, it's like they took everything I like and put in a single game. >_>