I think it’s more a complaint about the people not being cultured in general than it is a complaint about the country not having a culture (also, a bunch of the things mentioned aren’t culture but whatever).
https://dictionary.cambridge.org/dictionary/english/cultured
If all you know is cultural items from your own country I don’t think you can be considered to be cultured.
I think I’d agree with that, but that’s in reference to a person. A culture by definition must have its own cultural artifacts that aren’t simply taken from another culture. There’s also no requirement for those artifacts to be “high art”. Nearly everything listed in the OP is culture. So to clarify, I ask what you mean when you say “a bunch of the things mentioned aren’t culture”.
This is honestly a pretty ignorant take on america and its culture. A lot of our culture comes directly from the places people immigrated from, mixed with the culture that already existed. After a few generations it amalgamates into the broader culture. Its constantly evolving (whether people want it to or not). Its quite the opposite of only knowing culture fron our own country. In fact, a statement like that makes no sense when you factor in how peoole got here in the first place