I think the problem is that consumers may think they're treating their illnesses, but what they're receiving isn't guaranteed to be what they think it is. Another problem may be that consumers are self-medicating without knowing what they are really doing; not everyone who shops these sites is under the care of a medical professional.
Another problem is that not all of these consumers are just looking for cheaper versions of something they already take, some of them are looking for things they would never be prescribed at all, but think they need. If Dr. Acula prescribes you medicine X, but you really want to try to the stronger, better medicine Y that people on the internet forums are raving about, you may not know that your condition Z would make medicine Y dangerous for you. So you buy medicine Y online, it's all legit, not counterfeit, and works just like it's supposed to... and you get a terrible side-effect or worse. It's in the FDA's interest to prevent this situation.
There are also just straight-up illegal drugs for sale online, and they aren't available anywhere else for a good reason. Clicking through to the FDA report linked in the Reuters article, 110 of the sites are selling 2,4-Dinitrophenol as a weight-loss drug. The substance was banned in the US in 1938, and has caused deaths and disabilities in users. One problem is that personal tolerance varies widely. Someone looking for a quick weight-loss fix in an illicit drug sold online isn't likely to be very careful about dosing, or dosing may be impossible because the exact formulation is unknown.
I do agree that the prescription drug system in the US is very flawed, and it needs to be fixed. I also recognize that there are some people who would say, "let me bear the risk of what I put in my body" and resist government intervention in what they see as a private matter.
But, I think that the FDA is also trying to protect consumers from making uninformed decisions. There are certainly those in the world who know that desperate or uninformed people can turn to the internet to solve their medical problems, and it's easy for sellers to take advantage of these people. Since what these sellers are doing is already illegal, there isn't much of an incentive to provide top-quality products or expert medical advice. The consumers can't really go to the authorities if they are ripped off or poisoned, so there is really no recourse for them. I don't think that a desperate consumer looking for affordable treatments online would deserve a potentially fatal poisoning from illicit drugs.