Allow me to answer re your question about 'choosing' Medicare. 
Once an insured person reaches retiree Medicare age, their insurance company says enroll in Medicare, or we will drop you. Obviously as Medicare only partial pays, a person should carry secondary insurance, so they sign up for Medicare and many keep their old primary insurance as their new secondary plan (but their monthly premium does reduce in costs accordingly).
 *** Doubly critical is if the retiree has dependents like a spouse on their private health insurance plans. They must maintain the old plan as well then.