This is a funny one.
Complete and utter nonsense of course, but funny that there are people that actually believe it! The small fact that neither Jupiter or Saturn are massive enough to sustain fusion ... only a
tiny problem, really!
There is a set of videos from YouTube available by
Phil Plait, the Bad Astronomer from one of the TAM meetings a few years back that discusses this conspiracy theory and why it simply can't work. Actually, it's about the former version of this CS - for when Galelio entered Jupiter. Most of the problems relate to both though. It's a fun talk.
Part 4
Part 5
Part 6
Part 7
He starts talking about Jupiter/Galelio a bit of the way through Part 4.