Look, you have to draw the line somewhere. The more we look at life, the more the line between life and non-life blurs. Even if we do find a completely different "tree" of life that did not share the same genetic ancestry as the life we normally know, one could still make the argument that technically both "trees" are made of the same recycled nitrogen and carbon from the same planet, so it's technically one tree.
But don't stop there. If we find life on another planet, it's still the same tree. Both life on that planet and life on this planet probably share the same matter that came from the same supernovas.
As far as I see, trying to pin down this so-called "tree" thing is futile.