If someone follows a regimen to avoid the onset of a certain disease but still develops it, is that indicative of a genetic predisposition?

Yes and no: We all have genetic predispositions to diseases but we do not get all the diseases we are predisposed to. I suspect from your answer you are concerned about your inability to recognize people. Often the question is more important than the answer. If you ask the wrong question you are unlikely to get the right answer. There is an easy book by Dr. Amen, "Use your brain to change your age."read"

Not especially: but would need more information. The key point is the rarity of the disease. Sickle cell disease is highly clustered and was known to be genetic before even genes were figured out. Wrinkles are sort of genetic predisposition--can say that about everything including life and death. Then, diabetes is both entirely genetic and entirely controllable with starvation.

Yes: Almost every medical condition has a genetic basis. Family history of disease predicts genetic predisposition & increases one's risk however the road to development of a disease is much more complicated. We know that predisposition is influenced by multi-factorial elements eg. environment, diet, viral triggers, & more. Some diseases appear by spontaneous gene mutation showing no familial trail.