Horns of the Altar

Why grasp the horns of the altar when you’re a fugitive in the temple? How is it legitimate to touch the horns, when the altar as a whole is forbidden to all but the priests? The answer to the first is found in the premise of the second: The altar is holy, and communicates holiness to anyone who touches it (if they aren’t holy already). When a fugitive grasps the horns of the altar, he becomes sanctified and hence inviolable. If found guilty, he will be killed (like Joab) because of a sacrilege; but if he is innocent, he protects himself with a taboo of holiness.