Well, here's my opinion of it:
Faith healing can sometimes work.
Wait. Did I just say that? Did I become delusional? No. I'll explain.
It can work through the power of the mind. Not some mysterious supernatural deity.
If the person believes strong enough that he's healed, then he is. Or at least he believes he's healed, which has the same effect of shifting his reality.
It's also how placebo can sometimes heal people. (But it still sucks compared to real medicine when compared side by side)
Another example of the mind in action is when patients quit smoking with hypnotherapy.
A person who stops smoking after prayer is no different than that. Prayer is basically autosuggestion.
This also explains why God doesn't heal amputees. Because being amputee is a PHYSICAL condition, not a PSYCHOLOGICAL one. The mind just won't grow another arm or leg. Never going to happen.
So, praying to a tree has the same effect if you really believe it.