Obviously in order for the FE sun to work some of our RE assumptions about the sun must be wrong. And I have to agree with Tom here; since we've never been to the sun to study first-hand what's powering it, we can only really guess based on our observations. And some of those observations must be based on the assumption that the earth is round and the sun is 93 million miles away, since these were in place before we understood nuclear fusion.
The fact is that what powers the sun is anybody's guess in FE, which isn't that far removed from the truth about the sun in RE, since we have no way of knowing for sure (at present, at least) that we are right about it. People act like this is a violation of physics, but in truth our understanding of physics changes constantly; like Username implied, there could easily be an unknown mechanism powering the sun that (from an RE perspective, at least) mimics the effects of nuclear fusion.