Hello and thank you for posting your medical question on E health Forum.
Every patient is different and medications needed in each case differ.
Presence of just high Cholesterol is not a factor for medications to be initiated.
Other factors like age, risk of cardiovascular diseases , other comorbid conditions, etc are important when a physician decides to start medications.
In the case described, if a competent doctor with sufficient knowledge and experience did not prescribe the medication, though there were no contraindications for the supposed medication, and such a act results in morbidity or mortality of the patient, then a physician can be held liable.
If there was sufficient contraindication for the medication in a patient, then a physician would definitely prescribe other medications or suggest alternative methods to control the condition.
I hope this helps.