That's crap. A poorly reasoned, half-baked conspiracy theory. Yes, the family connections are there, but the movie
a. fails to mention that during Episode 4 the relationships between Luke, Leia, and Vader are still unknown. Therefore the "family ties" case doesn't hold up.
b. fails to take into account the power of the dark side of the force and the extent of the sway it holds over Vader. Even in Episode 5, when Vader understands Luke is his son, he STILL tries to kill him. Given (a), there is no way Vader could overcome the power of the dark side and sabotage the Death Star. If he did, his feelings would betray him and the Emperor would figure it out.
c. also misses the fact that Vader HAS to survive. It is his destiny. If he dies on the Death Star, there is no Episode 5 or 6. On the bright side, that means we never see the ewoks, but missing the Battle of Hoth would have been a bummer.
Conclusion: the premise that the destruction of Death Star 1 was an inside job is bullshit.
Ergo quod erat demonstrandum. Suck it, bitches.