That is not entirely true. Although dead blood cells in one of the pathways it isn't the only one.
Carbon monoxide in your body leaves through your lungs when you breath out (exhale) [1], Although Oxygen has only about 1/5 the affinity of CO to hemoglobin, there is power in numbers and if someone does get a very high dose, there are treatments. Hyperbaric tratments can save lives.
Experiments have shown that the half-life of the CO is about 300 minutes, but if the patient is on a non-rebreather, with high flow oxygen, this is reduced to 90 minutes, and under hyperbaric oxygen conditions, 100% oxygen at three atmospheres absolute pressure, the half-life is about 30 minutes. [2].
So if you or someone you know gets exposed to a high dose of CO, get them to a hospital ASAP.
[1] Toxicological profile for Carbon Monoxide
[2] Hyperbaric treatment of carbon monoxide toxicity