The reason you mistook my response for a strawman is the same reason you thought that the tweet was intelligent to begin with, because you misunderstand the situation. You think that it's not fair for me to point to other parts of his compensation package besides healthcare because you think it's automatically socialized healthcare since it's is paid with tax dollars. In which case, you could make the argument that it's actually communist since his entire compensation (not just healthcare) is provided by taxpayers. In fact, this would apply to all federal employees, especially federal employees receiving any kind of health insurance benefit (which is all of them).
Trump's compensation, and the compensation of all federal employees, including their healthcare package, is not "socialized" simply because it is provided by taxpayers. Taxpayers have hired these people to provide a service, and they have competed with the free market to do so. Trump's healthcare package is capitalist. It is provided by his employer for services rendered. It is the same reason that health insurance packages exist in any job anywhere. And this line of reasoning applies directly to all of the rest of his compensation, including his wages, the white house chef, the white house accommodations, the white house drivers and pilots... all of it. And it directly applies to all government employees. They're compensated in competition with the free market by their employer, the US government.