In a case like this, it is possible and even substantially likely that a "Cure" represents a treatment you can apply after an early, routine blood test but before clinically significant symptoms arise, to prevent damage from becoming significant enough to represent an illness.

Late-stage Alzheimers', if not every stage, is very likely going to involve microscopic-scale physical damage to brain tissue that is functionally irreversible.

Blowing up an asteroid after you can see it in the sky with your naked eye will not save you.

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It is also possible that what we call "Alzheimers" is actually biochemically five different disorders with distinct etiologies that have the same endpoint, and that it turns out we can cure two of them. Differentiating conditions for a biomedical catch-all category would be essential; "How accurate you can get the tests" is inseparable from this process of definition.