Let's make a better example:

You drive in to your car mechanic. You get a full on paint job, new windows, new wheels, new axles, the works. The car is shiny and new.

You come into the mechanic's garrage and say "can i have my car please" the mechanic says "your bill is XXXXXX". You respond with "nono i just need my cara, I'll pay you later...

And then when the mechanic doesn't return the car you complain "WHAT AN UNPROFESSIONAL JERK! PART OF DOING BUSINESS IS WAITING FOR ME TO PAY HIM!"

Analogy to health care:

A poor man with no money to spare is stabbed by a rusty nail. He will get an infection and die unless he gets massive antibiotics.

The hospital turns him down.

The reason we made LAWS preventing hospitals from doing this is because our healthcare is a piece of fucking shit. Most other countries the hospital would get paid in full by the government. Because health care != web design or car repairs!