Only national space agencies have had a reason to invest in keeping humans alive for long periods of time so they are the only organizations that have demonstrated that capability. It doesn't follow that SpaceX couldn't do it - they just didn't have a reason for it so far.

This idea that "life support" is the most difficult aspect is unfounded. The most difficult problem is transportation and reducing the cost of transportation means that you can attempt to solve every other problem by simply throwing more mass at it.

NASA does much of its work through contractors anyway and there are several companies working on independent space stations. I'm confident that the "life support is too hard" argument will be proven false in a few years.

A similar argument is made that "cryogenic fuel transfer has never been demonstrated at scale therefore Starship can't work". But nobody has even seriously attempted this! And the reason is that without reusable rockets every refueling mission is unbelievably expensive and the business case never closed.