No it doesn’t “depend.” You said “all other nations have single payer”- the fact is they do NOT. To say so is to be misleading.
Advocating single payer is a simplistic campaign slogan unless you really mean to implement that particular approach. And not that I disagree with it- but to say “all other developed nations have single payer” is false. They do not. Mostly, they have universal access of some sort.
The current PPACA (aka Obamacare) most closely resembles Switzerland except that the Swiss do a much better job of regulating the insurance companies.
I too want “universal access” and standardizing how we provide care by socializing the cost- we don’t disagree there. But- you can say it won’t matter what we call it- I disagree- I think we need to be factual and accurate and not blur definitions because once it hits the political sphere, that is when it falls apart if not specific and accurate. Republicans are masters (thanks to Frank Lutz) of framing things in a manner that skews debate — the less wiggle room you give them the better chance for success