I agree with you on this sentence. It is, as you said, a fact of medicine.
But your first sentence, that human illnesses, accidents, etc can be completely random is where I disagree.
It might not be a 2+2=4, but it's definitely not random. For each given disease, there are signs, symptoms, and other markers helping you to make the diagnoses. It's nowhere close to random.
(After all, medicine is a science).
Forgive me if this wasn't what you intended, but that's what I understood.