That's partially correct.
What the public option does is simply refuse to pay the market price. Then, one of two things happen. As do service providers with Medicare and Medicaid, the drug company may sell at the lower price to the public plan and increase its price to private plans. But, as our commenter suggests, that might not work if people migrate to the public plan in response to that and other costs shifted from the public option to private plans. The drug company, if it can, might refuse to do business with the public plan. But if it is legally required to do so or, if the public option by undercutting private plans, has become the only game in town, then it may be forced to take the lower price or withdraw the product.
In many cases, it may do the former because the cost of a drug is generally in its development and not in its production. Development costs are sunk. The company may not recoup its costs or make a "sufficient" profit at $10/pill, but it will cut its losses by selling it for that.
It's a bit more complex than that, as the health ministries can make a payment that covers more than the incremental costs of the drugs, meaning Canada is picking up some of the research and development costs.But without sufficient incentive to incur new research and development costs, patients might ultimately be able to buy only the cheaper red pill.
Here, too, I can quibble: a drug company could assume a larger standard volume, and quote Canada and everybody else a fully-allocated-cost price which would end the free riding. On the other hand, if the Canadian price makes some contribution to the development costs, Canadian patients and investors both gain by the contract. It's too late in the evening, and a thunderstorm is too close, to get into the intricacies of Ramsey pricing. Perhaps on another day.
We have now changed the economic environment in which new medical technology is developed. We have reduced incentives for development, so we will get less development. This creates hidden victims. We can congratulate ourselves that the $40 pill now costs $10. But we don't know who has suffered and died because the next pill was never invented. The only thing that we can be sure of is that it has happened.
This is why the "cheaper drugs in Canada" story is a canard. The problem isn't that the drug companies don't recoup their minimal marginal costs of production due to Candadian price controls. It's that they wouldn't have the same incentives for development if the whole world was Canada. In that sense, Canada's drug consumers are free riders. They enjoy what they don't pay for.
A "public option" is not the answer to unaffordable drug prices because it can't change the difficulty in developing new drugs. If we want people to have drugs that they can't pay for (and, at least for some drugs, we do), then we should help them pay for them.