Common sense
If there's one thing I've learned, it's that engineering common sense doesn't work any more when dealing with extreme conditions. The temperature at which iron melts doubles under 200GPa of pressure, about half of what you'd see at the Earth's core. The deep levels of Jupiter do strange things to gases. White dwarfs have diamond cores when they cool. I don't know what's going on inside the sun.
I'm really not buying the solids floating around inside the sun given only the evidence on that web page, but I wasn't going to simply toss it off based only on what I know about materials on the Earth's surface, either.