According to the Wikipedia, Draper was born in 1944, which mean that he ought to be covered by Medicare, which is the federally-run insurance program for individuals over 65. However, as other commenters have noted, even with insurance, it's not uncommon to find out that a particular procedure isn't covered by one's plan, and even very good insurance policies often don't cover costs 100%. For example, very good private insurance policies often only pay 80% of inpatient costs- the other 20% will be billed to the patient. That said, there's usually some sort of upper limit to the patient's financial responsibility, after which the insurance company pays 100%... but that limit can sometimes be in the tens of thousands of dollars, depending on the plan.

Furthermore, many insurance plans will cover a surgical procedure at one rate, but will cover ancillary costs (such as anesthesia, follow-up care, and medications) at a different (often lower) rate. This is all a long-winded way of saying that it is quite common for major medical procedures that are nominally "covered" by one's health insurance to end up costing the patient quite a bit of money when all is said and done. Look at the stats on medical bankruptcies in the US over the last few years- most of those people had insurance, and still ended up screwed.

Also, I'd like to point out that if Draper had been born a few years later (i.e., if he was younger than 65 years old) it seems quite likely that he might not have had any insurance at all. Many older people- especially people whose careers haven't been a stead string of stable corporate jobs, but have instead been independent contractors or otherwise self-employed- find themselves in the position of being 55 or 60 years old and suddenly unable to afford (or even be allowed to purchase) health insurance. Also, there are also quite a few people (especially these days) who are laid off from what had been formerly stable corporate jobs around that age, and find themselves uninsured for the first time in their lives just as their bodies are starting to break down. I know a number of people who celebrated their 65th birthday by going to the doctor for the first time in a few years.