They're referring to the original use of first / second/ third world countries which has nothing to do with economic prosperity or development, and just where they were in a war.
The doctor decides if you're ill and if so what treatment you get. If they want to brush you off and say you're fine, they can and do. Or they can decide if you get "treated" with a "take these painkillers and go home" rather than look at the cause of the issue.
If you're ill and turn to healthcare for help, but you get none, are you then recieving "universal healthcare"?
I suspect you understand this, but pretend otherwise.
I honestly had no clue what you were talking about when you said "Tell that to our doctors" in response to "Google says you have universal healthcare".
Honestly, what you describe that doctors do is the norm in the US and, as far as I know, most places. On top of that, we have to pay for health insurance out of pocket either partially or fully before receiving any treatment (premiums), when receiving treatments (copays), and after meetimg our deductible (co-insurance). Then they start to pay, but it starts all over again in the new year. So don't get sick if you have the budget insurance.
And then those insurance companies can limit the types of treatment the doctors can prescribe or make them jump through hoops before prescribing those treatments.
So .... Yeah. I'd like to have what Sweden's got.
Edit: I didn't even touch on PBM, private equity in clinics and hospitals, surprise billing, arcane rules to limit foreign trained doctors from practicing in the US, under funding of residency, not training enough doctors for our aging population and much much more