No, that wasn't my argument at all.
Maybe your habit of describing these things in "good" versus "bad" has stunted your ability to understand this situation.
I'll try just one more time: unless you're independently wealthy, U.S. citizens are subject to much the same wait times for specialized care as British citizens are -- or, I suspect, the citizens of most other first-world nations. And, again, unless you're independently wealthy, the quality of care in the U.S. is not any better than other countries -- and may even be worse, by some measurements. The usual counter-example that gets trotted out here are the various people that travel to the U.S. from abroad for various serious procedures; but, those people tend to be financially resourceful, and we're not talking about health care for the rich here -- we're talking about the level of health care available to most people.
In my technician's case, the "public care option" part of the anecdote merely covered most -- not all -- of the expenses after the fact. Short of having enough money to bribe hospitals and buy doctors, his experiences wouldn't have been any different if he were paying entirely out-of-pocket, or if he were covered by insurance, or if he were in his sixties and on Medicare.
The idiots that keep spreading FUD about "socialized medicine" keep trying to say that the quality of care will go down, or that our wait times for care will become terribly bad -- without bothering to notice that we aren't exactly the envy of the developed world in terms of either quality or speed. They also fail to ever explain exactly why a socialized payment system should have any negative impact on actual treatment; I for one would actually expect the opposite in a well-run system.
I'm pretty sure that all of the arguments against "socialized" health care pretty much boil down to, "the poor don't deserve health care", which stinks.