This article is stating a correlation but the reason they did this is that there is molecular evidence for cholinergic pathways in the body, and drugs which are anti-cholinergic, causing Alzheimer's because of this system being integral to the development of Alzheimer's disease.

The whole reason they decided to do this correlational study - and other studies like it - is because they have evidence that this cholinergic system plays a part in developing Alzheimers. Then, to back up that molecular theory and evidence, they're looking at correlations that the drugs that target this system have in developing Alzheimers. Sure enough things like how much one uses Diphenhydramine (active ingredient in benadryl and the same can be said for other allergy medications that are anti-cholinergic) shows that increased use has a direct correlation with increased risks of developing Alzheimer's disease.

Many studies on these anti-cholinergic drugs shows this correlation, they also have an understanding of the molecular basis of why, however in addition they also show that drugs that target this system in certain ways help reduce the symptoms of the disease.

Because of this, the evidence points to medications that fall into this "anti-cholinergic" or "slighly anti-cholinergic" drug category - allergy medications (diphenhydramine, loratadine) some PPI and others - might also amplify the chances of getting the disease.

There seems to be a lot of evidence pointing to this, and while its still an emerging area I'm confused as to how you are stating that this system and these drugs that interact with it, which has a lot of evidence that it is part of the disease pathophysiology, are weak on evidence?

What is your background and the experience you have to be able to state what you just said?

Here is some background on this system and its implications with Alzheimer's :

https://www.medscape.com/viewarticle/900644

"The Cholinergic System in the Pathophysiology and Treatment of Alzheimer's Disease"

"Cholinergic synapses are ubiquitous in the human central nervous system. Their high density in the thalamus, striatum, limbic system, and neocortex suggest that cholinergic transmission is likely to be critically important for memory, learning, attention and other higher brain functions. Several lines of research suggest additional roles for cholinergic systems in overall brain homeostasis and plasticity. As such, the brain's cholinergic system occupies a central role in ongoing research related to normal cognition and age-related cognitive decline, including dementias such as Alzheimer's disease. The cholinergic hypothesis of Alzheimer's disease centres on the progressive loss of limbic and neocortical cholinergic innervation. Neurofibrillary degeneration in the basal forebrain is believed to be the primary cause for the dysfunction and death of forebrain cholinergic neurons, giving rise to a widespread presynaptic cholinergic denervation. Cholinesterase inhibitors increase the availability of acetylcholine at synapses in the brain and are one of the few drug therapies that have been proven clinically useful in the treatment of Alzheimer's disease dementia, thus validating the cholinergic system as an important therapeutic target in the disease. "