It definitely cannot. I distinctly remember one of my professors in a physics class mentioning that no molecule that is known to man can survive on the surface of the Sun. The electrons are stipped away at those temperatures and the molecules disassociate into their atomic components.
So you're left with nothing but plasma (another state of matter) on the surface of the Sun. Not all stars are as hot as the Sun, of course, but the one in this article is... well, it's "Sun like," which means it's close enough.
This came up because he was telling us that no spacecraft could ever be constructed that would enable us to "land on," or explore the surface of the Sun, because no molecules can exist there. Our ship and all its instruments, and all the robots on board, would have to be made out of plasma, and it's kind of hard nowadays to image how you could possibly build anything like that. If there is anything that's impossible, that's it.
Or have some sort of protective force field we don't have a clue how to build.