It can't be discharged through bankruptcy (thanks Joe!), but neither can we squeeze blood from stone. Debtors who don't have the funds to both eat and make their payments will not make their payments.
Student loans haven't been something you can discharge in bankruptcy since the 1970s. If you want to thank a US president (as opposed to, say, the legislature that actually passes these laws), you should be thanking Gerald.
They are probably referring to then Senetor Joe Biden and his support for the 2005 Bankruptcy Abuse Prevention and Consumer Protection Act, which substantially broadened the set of student loans that could not be discharged in bankruptcy.
You can still discharge private student loan in bankruptcy until 2005, when a new bill pass to prohibit it. Joe Biden was one of the Democrats voting for it (as a member of the legislature that passed the law). The GP was probably referring to this
Joe Biden was a legislator for 38 years. He probably doesn't remember every bill he sponsored, but it's not as though he didn't choose to sponsor them.