Sure you can. You can not pay the extortion. When somebody is being robbed I don't blame them for having purchased video games in the past.
The line of reasoning you are referring to seems a little like questioning poor people because they got microwaves: "Why are you buying a non-essential item, dirty poor? Clearly you should be able to send your kids to college like a responsible person, if you can afford a $50 microwave oven. You're just not budgeting like an adult."
The insidious part about not having money to pay into an extorting system, is that you may very well have some degree of disposable cash at any given point in time, but still not enough to make dealing with the extortion practical. No matter how you scrimp and save.
The problem is one of sustainability. Almost everyone I know who does not have health insurance is more than capable of "budgeting". They feed themselves, keep their car maintained, buy fuel, pay rent. Most of them also see a movie or buy a small piece of entertainment once in a while. The money that goes towards those items is not enough to make a difference when it comes to buying decent health care - or enough to deal with the expenses you often incur even when your health care kicks in.
But clearly they are just not budgeting properly.
This of course has nothing to do with choosing not to pay into an extorting system because it's wrong. Which, personally, I also find a defensible decision, but realize that a vast number of people would be blind to that and simply blame the person in question for not being "responsible" like themselves.
The problem with the U.S health system is simple.
In other countries everyone pays a little (Well comparatively) for the healthcare in the country.
In the USA the sick whose able to pay, pays for the healthcare in the country.
For the completely healthy the U.S is great since they don't have to pay anything. For the poor the healthcare is great since they can't pay for it but that can't be refused so they get healthcare for nothing. For the unhealthy that can pay for it, it sucks since they have to pay a lot extra to subsidize the poor.
50 billion in hospital cost goes unpaid a year. Who do you think is making for it?
At the end of the day this is why you need NHS. Capitalism does not make sense for goods and services that can not be refused.
Because bootstraps.
Seriously, at times it seems as simple as that: to many Americans NHS is incomprehensible because they have been conditioned to see society in the most simplistic terms possible, where every man is his own castle and kingdom. Anything society provides to other people = that person taking something from you personally that they don't deserve. Make them go earn it themselves! Lazy bums. There seems to be somewhat little holistic thought in the American consciousness. Or consideration that society serves a purpose aside from enabling personal achievement and personal wealth gathering. Everything comes down to dividing us up into winners and losers, with capitalism as the referee and score tracker.
This attitude filters down to every aspect of life, including the right to basic health and bodily well being (in order to, you know, enable people to go out and achieve something in life. Or merely be allowed to live.)
It's all perceptual, as people have generally been conditioned to accept other communal services society provides, such as infrastructure and a military force that defends their status as a sovereign entity and the right to be pricks to each other.