Original Source of Snakes for Healing

The picture is the "Star of Life," which is the emblem used on ambulances.  What does the symbol represent? A search online says the staff and the snake comes from one of the Greek gods, a god of healing.

Isn't it more likely that the symbol originates with this week's parsha of Chukas? The Jewish people complained, and snakes came and bit them and they died.  Moshe prayed on behalf of the people and Hashem told him to fashion a snake and put it on a pole and whoever was bitten was supposed to look at the snake on the pole.  Chazal say, "Does a snake cause death or life? However, when Yisrael looked heavenward and subjected their hearts to their Father in heaven, they would be healed, but if not, they would waste away."