It really is true, as you say, that "every American has access to healthcare." I doubt you've thought this through, though, so let me explain it to you.
The bill for falling down and breaking your little finger, as I discovered last March, is about thirty grand--ER fees, exam, radiology, closed reduction (splint), orthopedic consult, surgical reduction (pin) with general anesthesia, physical therapy, and follow-up. The doctors would have eaten that bill if I'd been uninsured and unemployed. They've been eating such bills for decades. That is one very important reason it costs thirty grand to break your pinkie. The doctors can't get the money from the uninsured, so they raise their rates to compensate.
Of course they bill these higher rates to your medical carrier. This means that your medical carrier has to charge higher premiums to stay in business, if by "stay in business" you mean "pay its CEOs sums of money that enable them to live like medieval Pashas." This means in turn that your employer has to pay the higher premiums. This means he starts looking for ways to save money, such as cut staff. Now you and I are both unemployed, and not only that, jobs are scarcer for both of us.
Pretty soon (being unemployed) you're uninsured, and so of course you get appendicitis. Oh, man, that's a big one, chasing six figures. And now the doctors have to eat your bill, too, so they raise the cost of treatment for everybody again, and the carrier raises their rates to make up for that, and your former employer has to pay even more and fire someone else who then falls down or gets sick, and so on until nobody has a job and everybody is in the ER and we all choke to death in a tangled mass of MRI machines, paperwork, blood, bills, death, and lawyers.
Now you see from all this that you're already paying for everyone else's treatment. You're paying by being unemployed or by having your boss give you rotten looks and no raise, or by being out of a job. The only people who do well are the Pashas.
Back when 9-11 was fresh news, people were saying that the Constitution is not a suicide pact. Well, capitalism is not a sacrificial altar, and AIG is not God, and your life, both as to quantity and quality, is not Isaac. Oooh, irresponsible hyperbole! Until you get sick, anyway, or unemployed.
The idea of reform is: We can do better. That's a nice way to put it, because actually just about anything would be an improvement, including a poke in the eye with a sharp stick.