It's really important to not forget the genetic factors at play in Alzheimer's. Between 65-80% of all Alzheimer's patients have at least one genetic version of the ApoE4 allele, a genotype found in around 25% of the population [1]. ApoE is made in astrocytes and is involved in cholesterol transport to neurons and in repairing damage done to neurons that occurs with normal aging. That isn't to say there isn't a dietary link or that critical lifestyle factors don't interact with these genetics, however! Insulin resistance leads to inflammation (which has been shown to accelerate brain aging) and may be one way in which type 2 diabetes is linked with Alzheimer's. I think calling Alzheimer's disease "type 3 diabetes" may be a somewhat dramatic oversimplification and a bit misleading, though, since the mechanism would be a bit more general (in this case).
[1]: http://www.ncbi.nlm.nih.gov/pubmed/21787325