"Is it true the United States is the only developed country where not all citizens have health cover,"
Before Obamacare if someone was poor and had a big emergency, they'd get 100% coverage through "Emergency Medicaid." I understand from talking with ER doctors, that they routinely offered it in serious situations. If you are in this situation, go into the ER asking to apply for Emergency Medicaid.
If the situation wasn't big enough for EM, then the emergency rooms still have to treat the patient. No one is turned away. There is a bill that is sent afterwards and hospitals work out payment plans and/or write off alot of the balance for poor people. When hospitals hounded those who couldn't pay on large amounts, then they claimed bankruptcy to get out of it. Then, the hospital gets paid zilch. Of course, those "written off" costs made all of our costs higher. Hence, the need to increase premiums and Obama's push to get everyone covered.
To keep our local hospital ER's from being used as a doctor's office by the poor, they set up urgent care centers. They treat flus, colds, broken bones, infections, bee stings, labs, and normal visits, etc. Their prices are posted for the top 25 or so procedures for all to see in the waiting room, and are extremely reasonable. You can even get a payment plan there.
If you can't afford urgent care, then the county health office gives absolutely free treatment to the poor. They offer physicals, tests, pediatrician work, and even give out stop smoking stuff. You do have to wait a few hours to get in.
As far as pets, the Humane Society here gives very reduced price physicals, procedures, and even operations. If you can't pay, they pick up the tab.