The flaw there is thinking of that as an instantaneous event in time. It would be a very very gradual process as this source of mass slowly seeps into the atmosphere, the gravity slowly contracts the brown dwarf until the very core of it starts to fuse, then years as the heat generated slowly makes its way up into the upper atmosphere, disapating for eons into planetary weather until finally slowly beginning to radiate into the solar system.
You're correct, of course. There wouldn't be a big explosion like a nova. I was thinking of the instantaneous ignition of Jupiter in the book/movie 2010 - I'm surprised Arthur C. Clarke would have got that wrong.