I don't like either interpretation. But I can see Christ as the giving tree. As a child we had child-like faith in God. Then we grew up and wanted thrills. Later we were too busy or too cynical to be with the Lord. Finally when old and gray and too tired to run about, we find rest in him. Christ gave us the fruit of his labor, he cut off branches and grafted us in to his tree, and he allowed his body to be nailed to a tree for our sins. He gave us everything so that we could be in a constant resting relationship with him. But we needn't grow old to realize that.
I like this analogy the most. I doubt that's what Shel Silverstein meant. But sometimes good writers communicate truth in their art without even knowing it.