Trippier played the wrong pass and put Toby under pressure, a situation he was obviously less suited to handle. That speaks to his ability on the ball and playing out from defence, not his defensive capability. What you failed to mention, was his recovery to put in the tackle, and that spoke more to his abilities as a defender
Of course having more possession limits opportunities for the opponent and thus would affect your defensive performance. This is the premise of total football which is the foundation for the likes of LvG and Pep. One can argue for and against different football philosophies, but for me I care more about what you do with the ball than you having possession for having sake.
As to playing from the back vs hoof ball, I prefer a team be able to do both, as each has their pros and cons. As shown by the PSV goal, trying to play out of the back under a high press can have serious consequences. Under a high press, you would be better served hoofing the ball and having people upfront that can win the ball. A high press leaves the opposition midfield undermanned and can easily be exploited if the ball is delivered into the final third quickly enough. Even if you lose possession, it is far from your goal than losing it in your own 3rd. Summary, build from the back when their is no press, but hoof the ball if the high press is coming.