People at various points in the ideological spectrum have pointed out it's a little odd to see conservatives objecting to the idea of the government deciding what medical procedures ought not to be covered, when they're apparently okay with insurance companies deciding what procedures ought not be covered, or with people not being able to afford procedures because they lack good insurance. However, it strikes me this difference may actually make a fair amount of sense, both for some pragmatic reasons and some emotional/ideological ones.
There are lots of insurance companies, and when polled people often rate their own pretty high. So many people may not expect to ever have problems with their own insurance companies refusing to cover something vital. However, people (conservatives especially) don't tend to trust the government very much, and there's only one. So people who hear about insurance company problems can tell themselves (rightly or wrong) "It won't happen to me." But if the government decides to block something, everyone knows it will effect him.
With insurance companies paying for care, one can always try to use public shame (driving away customers) or lawsuits, or government regulation to make them provide some service you think they owe you -- however if the government is making those decisions people are probably more skeptical of their ability to appeal to the government to get the government to reverse its decision on something. (Most people have experienced this with disputing a cop's version of a traffic stop, or trying to get an appeal through the IRS. It's not easy.)
It's often slow to get government programs to change rules even when it could save them money -- while private enterprises have more obvious incentive to do this. For example, my mom and her parents recently struggled with a rule in my grandfather's veteran's benefits that they would only cover a stay at a rehabilitation facility after a stroke if he'd been in the hospital for at least three days first. This despite his doctor insisting he didn't need to be in the hospital three days, he was ready to be discharged so long as he could get rehabilitative care.
Conservatives at least (liberals seem to have a greater tendency to be deterministic about these things) tend to figure that since insurance is something you buy that if it doesn't cover what you want you could always buy something else. The government saying "that's not covered" simple feels more final to people.
Upsetting as they may be at times, your insurance company in some sense works for you. American consumers have a strong sense of their rights as consumers. (If you doubt this, try getting service at a business in the UK and note the difference.) Few people manage to feel that the government works for them. It does, after all, have the power to arrest your or fine you if you get out of line. Most people would rather fight a customer service rep than "fight city hall".
People prefer making hard choices themselves -- even if it's not much of a "choice". "There's a very experimental treatment available, but the chances of success are low and I don't want to bankrupt by family" has a certain nobility to it. It sounds like you faced a hard choice and did the stoic thing. "There's an experimental treatment available, but a government panel decided that it didn't provide sufficient increase in life expectancy so it's not available in this country," sounds like the system stuck it to you. (This is probably one of the biggest emotional differences between conservatives and liberals on the issue, since it seems that many liberals feel like it's being stuck to them by the system when a company won't sell them something affordibly, but consider the government to be an "us" with only the common good in mind rather than a "them" mostly interested in itself.)
Robert Louis Stevenson, Kidnapped
1 hour ago