She's confusing how accrual accounting works. Student debt cancellation would cost the government money.
Some CBO estimates show that the government expects a loss on student loans, but those estimates are based on the net costs over the total life of the loan, including future repayments and expectations on defaults/subsidies/interest rates/etc. If we cancelled those loans today that'd be an immediate large loss on the remaining loan balances.
In any case those estimates are noisy too. Some years they show profit, sometimes losses. And they vary by loan type and borrower.
The government these days does own most of the outstanding student loans. They aren't always the servicer of that debt. Some companies are paid a fee to service the debt. But I believe about ~90% of outstanding student loans are owned by the government. The ACA made them the owner of all future loans, and before then they were a good chunk of it. And it is my understanding that the President could unilaterally cancel the remaining loans. But it would incur losses for the government.