Therefore securities built on top of these loans, such as the pools you refer to in your link, are by definition not "asset-backed-securit[ies]". They are instead backed by e.g. the laws and regulations that make them non-dischargeable ... and I contend that's a major reason why they are non-dischargeable.
The student loans themselves are assets (the fit the above definition), my point is that they themselves are not asset based like a house or car loan.
Sallie Mae's use of the term "asset" here might be slightly misleading, but being essentially part of the government they can get away with it.