About 16%[1][2] of Americans don't have health insurance. While the situation you describe is tragic and too common, it is a gross exaggeration to say it's "typical." Someone unfamiliar with the United States would read what you wrote and assume that this is the usual situation, when in fact it is relatively rare.
Should something be done to help that 16%? Yes, of course. Is it common? No.
This does not tell us that it's "typical" for those with health insurance in any sense. It tells us only that bankrupcies of insured people are often caused by health bills. This does not imply the inverse, that insured people's health bills often cause bankruptcies.
This is reasoning backwards: you are starting with the conclusion you'd like to see (that bankruptcy is typical for people with health insurance), then trying to adapt the evidence to fit that conclusion. Let's try it the other way around, looking at the data first, and then drawing conclusions:
There were about 1 million non-business bankruptcies in the US in 2013[1]. Reuters says that 60% of them were caused by health bills, and of those, 75% had insurance. Taking the bankruptcy and the Reuters figures at face value, this gives us about (1m * 60%) = 600,000 bankruptcies due to medical bills in the US annually; and of those, (600k * 75%)=450k had health insurance.
Going by the earlier Census.gov figure that 16% of Americans are uninsured, and a US population of about 316 million[2], this means that about 265 million Americans have health insurance.
We can then calculate that of those American who have health insurance, only 0.17% (450k/265m) wind up in bankruptcy due to medical bills; in other words, 99.83% of Americans with health insurance do not wind up in bankruptcy.
I think we can thus safely say that it is definitely not typical for an American with health insurance to wind up in bankruptcy due to health bills. It does happen, but it's very rare.
That's the yearly percentage, not the lifetime percentage. The chance of something happening to someone in a given year is vastly smaller than the chance of something happening to someone during their life.
So if 600,000 medical bankruptcies a year happen, how does that compare to other yearly numbers? Well, there are about 4 million births a year in the USA, so someone being born in the USA happens only 7 times more often than someone becoming bankrupt through medical bills.
It may have been slightly inaccurate to use the word typical, however these figures seem to indicate that it is at least fairly common.
Should something be done to help that 16%? Yes, of course. Is it common? No.
[1] http://www.gallup.com/poll/168248/uninsured-rate-lowest-2008... [2] http://www.census.gov/content/dam/Census/library/publication...