First off, Vietnamese don’t consider 褘翟衣 as their traditional dress, but historical dress. The dress 褘翟衣 has been out of tradition since Lê dynasty, so it was no longer passed down. “Tradition” is when something is passed down to this day, and 褘翟衣 was no longer passed down in Vietnam.
Second, Koreans deserve the right to call 褘翟衣 as their traditional dress, more so than China. Yes, the dress came from Chinese, but as I said, “tradition” is when it is passed down. In China, 褘翟衣 had been discontinued the moment Qing dynasty was founded. The dress was no longer tradition, only the headdress 鳳冠 was passed down through wedding dresses of Han Chinese women. So in a sense, 鳳冠 is tradition, but 褘翟衣 is not, as it is historical dress.
Koreans, on the other hand, preserved 褘翟衣 all the way to the end of the monarchy, and still retains plenty of artifacts. This dress’s final moment was in Korea, and existed until the beginning of Westernization. So yes, 褘翟衣 is Korean tradition, as it is still passed down.