It is indeed true that H.H Dalai Lama can end all of these controversies. The big question is what doesn't He do that?
Why create schism within your own Buddhism school and make friends with other religions? It doesn't make any sense at all. It shows nothing at all. It will be pointless for that kind of courtesy to try create peace within different religions. Simple reason, even within your own religion you are not able to create peace and harmony why extend the gesture to other religions?