Did the Washington Post call the imposition of work requirements for TANF an increase in government regulation? Does it call restrictions on funding for Medicaid abortions an increase in government regulation? This is not the framing that the Washington Post typically uses for rules governing access to federal programs. The federal government is giving out the money, it gets to set the rules.
One then has to ask why the Washington Post chose to use this convoluted framing to discuss the Obama administration's effort to impose limits on the schools for which students can get federally subsidized loans. The limits require that to be eligible to receive federal loans through this program, a school would have to maintain a minimal record of placing its graduates in jobs.
This is a measure designed to protect both students, who will be on the hook to pay off their debt, and also the taxpayers who will have given money to the school for no obvious public goal if it does not help graduates get jobs. In the absence of this sort of restriction, schools like the one operated by the Washington Post's parent company, will be profiting at the taxpayers' expense, effectively getting public money for nothing.
In this respect it is worth noting that the regulations would impose no restriction whatsoever on where students could go to school. They would only restrict the schools for which they could get federally subsidized loans. If Kaplan and other for profit colleges think that their schools are good investments for students then there is nothing to stop them from making loans to the students themselves.
It is understandable that the for-profit college likes to frame this issue as one of government regulation, but it is hard to see why an independent newspaper would adopt this framing of the issue.