In bankruptcy, student loans are not dischargeable unless the borrower initiates and can prevail on a separate lawsuit to determine that it would be an undue hardship to pay it back. Courts have interpreted this to be a relatively high standard, virtually impossible in most cases. A separate line of litigation can involved whether the loan is actually for an educational benefit.
The US Supreme Court accepts very few cases. By declining to accept this case, the difficult standards of the student loan issue, and whether bankruptcy remedies can be eased, will be up to Congress.
Here is a link to a good article about this case.