Mr. Tagert had ALS for 6 years. After a heart attack he became completely incapacitated, able to communicate only with his eyes. He preferred to be at home, instead of at a medical facility where he would have had 24-hour care (he would have lost custody of his 11-year old son if he was moved permanently out of his home). The Canadian government offered to pay for in-home medical assistance for 20 hours per day, but Mr. Tagert arguably needed 24 hour care. If he in fact needed 24-hour care, he would have been responsible for paying for the remaining 4 hours, or, he could have agreed to be moved to a 24-hour care facility. Instead, he chose to commit suicide.
Under this scenario, I'm not sure a different outcome would have occurred in the United States. Private insurance would have covered some of the expense, but likely not all, of 24-hour in-home care, given that 24-hour care would have been available in a 24-hour care facility. Mr. Tagert would have had similar choices -- the difference is that if he made the same choice in the United States, he would hot have had the assistance of his insurance company or doctors.
I'm not for or against a single-payer system, I'm just pointing out that difficult facts make for difficult choices, and there isn't anything in this story to suggest that private health care would have offered better options. I don't think it's fair to say, as you imply, that the Canadian government agreed to pay to kill Mr. Tagert, but wouldn't pay to take care of him.