That's a screen capture from the KBS documentary addressing the origin of the family name "Kim". Check the URL of image.
It was always known that Kims were a little different from the majority of Koreans from Northern Mongolia, that they were descendants of Xianbei(The spin-off branch of the Huns that the Han Dynasty battled for ages) who also ruled China as Sui/Tang emperors. So you have the general Korean population from Siberia whose closest relative is Evenki, and the "Kims" who are the descendants of Xianbei.
As the so-called Southeast Asian blood, those are the ones that's flooding in right now via mail-order-brides, and those farmer's children born to Chinese, Vietnamese, Filipino, and Thai mothers do look different from pure-blood Koreans, so a lot of sociologists are concerned by the future race war between pure-blood Koreans and mixed blood Koreans/resident immigrants numbering in millions that are exploding in the countryside.
So where is the URL of Korean article or webpage where the claim that Atila was Korean? I actually know that story, and it came from Germany, not Korea. Why German archaeologists said in German documentary that the Huns originated from Korea is based on artifacts from Sillia King's graves, which is strikingly similar to Hun artifacts. It also presented big problems for Korean archaeologists who were finding Roman glass and very European looking swords from the Silla King's graves dated 4th century. But once again, that similarity can be explained by the Xianbei connection.
Koreans don't call Chinese brothers; they call Mongols and Turks brothers.