I was under the impression that private student loans were also guaranteed by the government, but based on my searches trying to source my information, it seems Obama administration changed this since I went to college.
The government under the Obama administration changed things so that "Federal" loans instead of being made by private organizations and backed by the government, were directly distributed from the treasury.
However even before this, there were separate Federal and private loans, and the only way to get to $200k (for undergrad) was to get unsubsidized private loans that weren't backed by the government.