IMHO Davey already knows what he wants to know about everyone on the team. He didn't take this job unprepared.
I agree that he isn't clueless about the players on the team, but he hasn't really been around them during actual games, so the input of the coaches who have a first-hand day-to-day experience with them is going to be factored in. Also, I would imagine Davey's not stupid enough to simply blow off the opinions of the assistants he inherited day one. I do think Davey's tendency would be to push Lannan, especially with a taxed bullpen. But to ronnynat's point, during Lannan's last inning, it did appear to me at the time that Davey was on his way up and out of the dugout when McCatty started to weigh in and he stepped back. The combination of needing one out and the taxed bullpen had something to do with it too.
In the end, Lannan needs to learn to do what he has to do to keep control of his mechanics and battle out of those situations. So, it isn't the worst thing to push the guy. I think in terms of just trying to win every game, most of us have gotten used to seeing the managers yank the pitchers one or two batters too late.