Interesting, you use the word "purely" to dismiss the observation out of hand without responding at all.....
Most people use words to frame their thoughts, and so one's choice of words affects what thoughts might be available.*
To me, the concept of "single payor" is both well-intentioned, and also a covert way to infantilize people...."don't worry, mommy and daddy are here to take care of things for you." Highly-cynical people often use the lure of "free" goodies deliberately to inculcate a sense of dependency in people who do need help. However, rather than "help" them through a difficult time while also helping them learn better to care for themselves in the future, the "help" comes with a very serious "string" attached: you can only continue to receive that "help" as long as we are in power to give it to you.
People rightly criticize capitalism for its inherent tendency to divide society into "haves" and "have nots" yet progressivism does exactly the same thing: either you run the government (and get to ride around on fancy airplanes at taxpayer expense) or you depend upon the government (or I suppose you turn over half of your income to the government for the privilege of having such a wonderful government in charge of your life).
It seems to me that any viable healthcare system must include people taking responsibility for their own outcomes. There always has to be at least a dual-payor system (if not more): the individual him/herself, and some other funding source.
* not sure how many people have learned a foreign language as an adult. Typically, one subconsciously assumes that the other person "really" is thinking in your language, and only is speaking their language. At first we translate their words into our language, formulate our response, and then translate back into their language again. Once you become fluent in the other language, you actually start to think in that language as well. When you do, you generally find that there are certain words that just can't be translated: you start to say "it's sort of like..." followed by a sentence or two.
I recall visiting a friend at work who worked for KLM Royal Dutch Airlines. She was talking on the phone to someone from headquarters in Dutch, then hung up the phone and started speaking to me in Dutch as well. It was only when she saw the puzzled look on my face that she asked, "oh, am I still speaking Dutch? I'm sorry." She was not consciously aware of which language she was speaking.
I guess this is an extremely long-winded way of saying that "yes, it is semantics" and also "no it is not 'purely' semantics."
One of the challenges I have from time to time is that I also learned to think in symbols, and it can be tricky to translate symbolic thinking into any language using words. It was eerie when we were moving and I found my old quantum mechanics notebood from college. I recognized my handwriting and knew that I could manipulate all those symbols at that time, and had lost the facility of that due to lack of constant use.