Please cite something that explains this fully. The government does back and will pay the loan on default, but then it is the government that attempts to collect. The lender is not getting paid twice.
My problem with all the complainers of student debt is that everyone who took that loan knew what they were signing. I'm tired of hearing the sob stories of people who go to an out of state school, do not work, live completely on loans in order to have the 'college experience' and end up 100k in debt. No private lender would ever lend an 18 year old money for that and it is only possible because of government backing to start with. The government wants to recover at least of portion of that money, hence the rules.