That’s literally how new things came to be in every larger culture. Sushi didn’t magically come into existence across all of Japan simultaneously. Rice techniques were continually improved upon and exchanged throughout the hundreds of cultures across Asia.
Welp. It didn't even originate in Japan specifically.
If I take yoga, and call it something else without actually changing the fundamentals and say it is superior, that’s appropriation.
A restaurant was protested for cultural appropriation because the owner was white and it was serving Sonoran recipes under the original name. It was just the fact that a white person was profiting off of that particular subculture that made it appropriation.
Ever think the whole thing is just making a mountain out of a mole hill since it's never the "offended culture" that's ever offended, but some random person in San Fran or Los Angeles without a real job?
Consider white girls at music festivals wearing bindis as a fashion statement. I don't think this fits your definition, but it is a popular example of cultural appropriation.
adpropriare "to make one's own," from Latin ad "to" (see ad-) + propriare "take as one's own,"
It means that I take something from culture X and pretend that it is from my culture, and/or in some cases twist it so that it makes my culture seem more superior.