Actually, that’s not necessarily correct that they would have to borrow.
If a person has been putting every penny towards student loans, then that means they are paying more than the minimum which means they are technically paying ahead (their min monthly payment for the next month(s) may be as low as $0).
This means that if they continue paying more than the min, they will pay less interest on their loan. But it also means that if they have a really big unexpected financial event (like a car breaking down) then they will be able to SKIP a payment towards their loan that month (and for however many months they are paid ahead).
But even before skipping a payment, they can divert the net cash flow money that was going towards paying more than the minimum and instead apply it towards their car repair.
I agree that it is important to have an emergency fund, but (based on the numbers) I believe it is valuable to pay more than the minimum towards student loans, especially earlier in the loan term.