This is 100% wrong. There are cases of monogenic type 2 diabetes (e.g MODY) which has a similar inheritance as the Alzheimer's case in the story. Though rare, it certainly refutes the 100% assertion.
The primary goal of a PhD is to provide training for independent research, and honestly it really does require 4-5 years of dedicated work to achieve that (I have a PhD in computational biology). Teaching is different altogether and absolutely does not require a PhD. Proving that you can perform independent research really does require many years of training.
This is a gross oversimplification. Diabetes (particularly type 2) is a complex disease with both environmental and genetic factors. I'm a T2 diabetic and was diagnosed while having a low BMI (20) and reasonably healthy lifestyle. There wasn't much I could actually change about my 'lifestyle' -- no weight to lose, etc. Medication was the only solution and not surprisingly made a significant impact.
"Type I is genetic. If you have the faulty genes, you get it. Regardless of lifestyle, health, country and whatnot."
Also, this statement is not correct. From OMIM on type 1:
"IDDM exhibits 30 to 50% concordance in monozygotic twins, suggesting that the disorder is dependent on environmental factors as well as genes. The average risk to sibs is 6% (Todd, 1990)."
There are other studies with similar conclusions. Having the "faulty" genes does not guarantee disease manifestation because the disease is multi-factorial.
I'd like to add that there isn't always a clear cut delineation between the types. For example, MODY is highly penetrant, heritable diabetes that fits neither classification. The idea that type 1 == genetic and type 2 == external is really no longer the prevailing view. The better description is the production of insulin where in type 1, there is a lack of insulin production and typically in type 2 insulin resistance (and possibly deficient insulin). The causative factors are complex and a combination of genetics and environmental factors. I'm a type 2 diabetic with none of the traditional risk factors (typical diet, and underweight), from a family with a high diabetes frequency (sister and father).