I could be wrong, but I always thought carbon monoxide poisoning worked the following:
The the bond between heme and CO is stronger than the bond between heme and oxygen. The bond is much weaker for CO2 and heme.
The strong bond between heme and CO, results in the body taking in less oxygen. As the lungs do not exhale CO as efficiently as CO2, because of the strong heme and CO bond.
20% oxygenated air is not sufficient for the body, when poisoned by CO.
I suppose La Chatlier's principle affects the desorption of CO from the blood.