This seems very wrong to me but perhaps I am mistaken

You are very much not mistaken. I talk quite often on this sub about Bald's Leechbook, a 9th Century English medical textbook, likely produced during the 'Alfredian Renaissance' of the 870s-890s. Named after the patron who commissioned it, a Leechbook is quite literally a 'doctor-book' and contains a combination of a wide array of classical medicine and contemporary herbalism that proffers a wide array of treatments for diverse wounds, illnesses and infections. Although its prescriptions may sometimes seem odd to a modern audience, the Leechbook was largely based on contemporary observable scientific evidence, and genuine botanical or medical science does underpin a lot of its treatments. Famously, a salve it recommended as a treatment for a stye in the eye was found to be effective recently against MRSA infections. Bear in mind that, without modern scientific medical knowledge, treating the symptom of a disease would often be synonymous with curing it. It certainly would have been news to a 9th Century English physician that they weren't meant to be actually curing anyone, given that their Leechbook's contained any number of treatments designed explicitly to cure conditions.

Chapter 40, for example, contains treatments for disorders of the spleen, and states:

Again, when the spleen becomes inflated it will immediately harden and then becomes difficult to cure, when the blood hardens in the veins of the spleen. Treat him then with the aforementioned herbs, mix the good herbs with oxymel, the Mediterranean vinegar drink that we wrote about before, that heals the spleen and does away with the thick and hepatic blood and the harmful humours, not through urination alone but also through other excretion.

Treatments for wounds explicitly reference the importance of washing and cleaning a wound in order to prevent infection, and also contain a number of cures should a wound become infected, even going so far as to advise on proper technique for amputation should a limb turn gangrenous. In this context, disease is clearly something that can, and actively should, be avoided, limited or rapidly cured at all costs:

For the cleansing of a wound, take clean honey, warm by a fire then place in a clean vessel, add salt to it and whisk until it has the thickness of a paste, smear the wounds with that when they grow foul.

Phrasing throughout the Leechbook continuously refers to disease as something to be actively cured, nowhere moreso than in its contents pages, which list extensively what cures for which diseases and infections can be found therein, such as:

1.36: Treatments for the disease that is called shingles, a paste and drinks and salves; that is a very dangerous disease and it dictates here which food or drink one should forego in that disease.