The ball is clearly fair. The umpire clearly signals the ball dead. The Dodgers played through the dead call and the Padres did not. I'm also positive had the sides been reversed (Dodgers on the bases) the Padres would have been the team that played through the dead ball call.
So what we have is the defense playing through the play regardless of what the umpire says or does. The catcher may not have been able to see the home plate umpire (he was behind him!), but I'm pretty sure the umpire would have verbalized the play in some way. Regardless of whether he did or not, the rest of the fielders saw the umpire signal the ball dead and still threw the ball around the horn for the triple play.
This type of play sucks. On one hand I'm thinking the play should be over. The umpire signaled it as such so the Padres not running makes sense. On the other hand the Dodgers ignored this and played through it. On one hand you have a premature call that shouldn't have happened and on the other you have one set of players that let the play develop. Let's face it. Once the umpire calls the play dead the runners are going to stop.
However, I have spent years arguing that MLB needs to get more plays right and it's because of that I can't argue that the wrong call was made here. The ball is fair. The Padres, like the Dodgers did, could have disregarded the umpire's signal and played through it. And that is what should happen in the future in my opinion. You've got one side playing and asking questions later and the other side not. It's an obvious disadvantage.
Had the ball been ruled dead and the runners sent back to their bases, the Dodgers would have been pissed and rightfully so. They would have gotten 2 on that play had the Padres run. The ball is ruled fair and the Padres are rightfully pissed. But the end result is that the correct call was made and the side that disregarded the umpire's initial ruling was correct in doing so.
The baserunners should play through similar plays just like the defense does.