Are you speaking about the US as a whole or just the federal government? If you only consider federal income taxes, then yes, our system looks progressive by comparison. However, US citizens pay federal, state and often city taxes and the tax rate become more flat in many locations when all levels of taxation are considered. Also, for the full picture, you really should consider benefits. For example, even as someone with no major health problems, my health insurance and healthcare costs between 10% and 20% of my pre-tax income - as it does for many Americans. Other nations have comparable healthcare systems that are funded by taxes, so excluding that benefit skews the comparison.
While I gave Sweden as an example, I was initially comparing against Canada as that's where the topic came up in the discussion I had. We also have some flat income tax provinces too. A straightforward comparison would not be easy.
Everyone pays in a solid fraction of their earnings, and when in need, the state steps in and pays.
This routes around the case where people saves nothing and have be bailed out, while those who do save get nothing.
They are also quite pleased with how supposedly socialist America already is. It seems almost like a reverse psychology trick.