Try to hit yourself by looking up with any arrow and use your bow very quickly or use it one time the fastest as you can. You will see that the arrow just pierce you without damaging you. This doesn't look to have too much sense, so I posted this because this behavior it's very likely to be a bug.

Also, this doesn't seems to be related with the arrow immunity-time behavior, because it happens every time with the "lowest-leveled" shooted arrows (with lowest leveled I mean the lowest and fastest level that a bow can have to shoot arrows).