Is it common in the US not to pay medical bills? Or do I misunderstood what had been said?
I would feel comfortable saying that most people who face medical bills don't pay them. They are unable. If they were able, they would have gotten medical insurance. In America, something like 55% of individuals do not have even $500 of savings, so when a big medical bill rolls in especially on top of lost work hours, they don't have a lot of options.
The hospitals are trying to rip them off
Hospitals charge reasonable prices to insurance companies and Medicare. These fees are negotiated in advance and reflect the hospital's actual costs. This is called "usual, reasonable and customary".
Hospitals charge a wildly inflated, criminally outrageous "cash price" to the uninsured. For instance back when Medicare paid about $175 for an ambulance ride, a friend was billed $1100 for the exact same thing. The hospital aims to scare the living daylights out of the patient (caring nothing about what that does to their health!) Perfect world, the patient pays them the $1100 instead of paying their rent. If the patient puts up a fight, they hope to haggle them down to something like $400, remember it really costs $175.
This tactic is a huge profit-center for hospitals, even the "charity" hospitals, and they feel justified because so many uninsured don't pay at all (the hospital considers them "deadbeats".) Well, patients don't pay because cash prices are unreachable, so they just give up.
Anyway, your friends are correct, don't even think of paying those cash billing amounts. Research and find out what Medicare pays, offer 60% of that, and haggle it to 100%. And sleep well knowing you paid what is fair.
Not all services are as overpriced as my example, but most are at least 50% too high.
Or you may have misunderstood what they said
The hospital does send you all the bills as a formality, even while they submit them to your insurance company. And then the insurance company usually pays them, so it is correct to "not pay that bill".
A lot of medical offices will check with your insurance company even before you leave the office, and ask you to immediately pay anything the insurance won't cover. For instance they often have "co-pays" where you pay $20 and they pay the rest.
To be clear: if your insurance company negotiates a rate with the hospital, say $185 for the ambulance ride, that is your price, which you are entitled to as a member of that insurance system.
Yeah, it's that complicated
A lot of people get their livelihood from the inefficiency in medical insurance and billing. Their political power is why it's so hard for America to install a simpler system (or even replace Obamacare in an ideal political environment). It is also a big part of why America spends 18% of GDP on healthcare instead of 7-11% like our European peers who do not have to account for every gauze or rebill multiple insurers. Sorting out "who pays" would be expensive even if everyone did pay.