Can you speak in just pure Korean?

The Koreans in the video below were first asked how well they thought they could speak Korean, their native language. They all answered pretty confidently that they could speak Korean "well" or "as well as any average Korean." However, when they were asked to answer some simple questions in Korean without using any English loan words, they had some trouble.

One of the things that surprised me about the people in the video was that none of them seemed to know the Korean word for menu. When I was in Korea, I remember seeing the word 차림표 on wall menus in more than a few Korean restaurants, so I do not know why they had trouble with that word. In fact, when I was learning Korean in Korea, I used to write down words I would see in public that I did not know, and I think 차림표 was one of the first words I wrote down.

Also, when I was in the U.S. navy stationed in Korea, one of my shipmates told me a story about another navy Korean linguist who had just arrived in Korea. He said they were in a noisy Korean bar together and needed some ice, so the new guy, wanting to practice his Korean, called the Korean waitress over and said, "얼음 주세요," but the waitress didn't understand him, so he repeated, "얼음 주세요, but she still did not understand him. Finally, after the new guy had tried a few more times, the guy telling me the story told me that he looked at the new guy and said, "Let me try." Then the veteran Korean linguist looked at the waitress and said, "아이스 주세요." He said the waitress then immediately went and brought them some ice (아이스).