That's a rather pat explanation that doesn't seem to explain things such as the rampant rise of tuition at state colleges and universities.
The budget problems in states then force the issue.
Federal subsidies aren't the only reason for higher-educational inflation but there are growing hints that subsidies get largely captured by fee-increases. See for example these discussions:
http://www.bloomberg.com/news/2011-12-09/u-s-universities-fe...
http://www.mindingthecampus.com/originals/2012/02/why_they_s...
Similar to the cost of health care in the US.