I hope he does have access to more data than me, otherwise I'd question what the hell the Washington Capitals are doing!
If he's doing something and it's for a good, valid reason that will lead to more wins either now or more importantly in the playoffs, then I'd say great! If having a tight leash on Evgeny Kuznetsov and Jakub Vrana now will make it so that they are better players in the playoffs then great!
But Vrana had limited ice time in both years under Rierden in the regular season, and that certainly didn't help him in the playoffs. Why would that same strategy work under Laviolette? I suppose it could, but I don't think it should be the default assumption. And whatever Laviolette is doing now is certainly not working in terms of protecting multigoal leads in the regular season. Why would the current strategy work in the postseason, but not the regular season? Again, I think some of that is goaltending, but the Capitals also completely abandon attacking once they get a lead, especially in the third period.
As I have mentioned I think the far more likely explanation is not that Peter Laviolette has a private set of data that only he and the Capitals staff are privy to and that this data indicates that Vrana and Kuznetsov should get benched in third periods with a lead (the opposite of what publicly available data says), but rather that he just prefers vets and is harder on younger players. The reason I believe that is because the vast majority of NHL head coaches prefer vets and are harder on younger players, no matter how much better the younger players might be at accomplishing the goal of winning hockey games.