This is indeed a difficult situation: on the one hand you're concerned for the reputation of your school, and in turn, how that reputation might affect your chances of being asked to return after the internship has ended.
However, there are some considerations to take into account. First, it is not your responsibility to protect your school's reputation. In doing so you could potentially open yourself up to some issues of your own.
Lets for example assume that you discuss the issue directly with your immediate supervisor and the reason for this person leaving early is serious, or personal? It could convey particular characteristics, namely that you are not trusting, or do not necessarily work well with others etc.
It is also worth noting that this individual may have lied about their reason for leaving work early, but it was accepted by their employer that they could, in fact, leave early. This means that aside from this interns reasons being false, they did not necessarily break any company bylaws, or rules.
There are instances where, as an employee, our reasons for wanting to leave work early or indeed take time off may be of a personal nature. We might deal with this by creating a white lie to cover the real reasons, or by simply explaining that the reason is personal and asking for the time anyway.
In this instance the main problem is that you were made aware of the real reason behind them asking to leave early. Although you take issue with this it still doesn't make it your problem to resolve. If this person continues to slack off, take time here and there, he/she will eventually be found out. Hard work pays off and that's the real fact of working life.
Should this interns behavior deteriorate further, then you could consider talking to your institution rather than the employer, this would perhaps be a more appropriate action to take. It may allow you to control the tone of the conversation as it may be with a professor (teacher, educator) that you are familiar with.
tldr: This is an issue between that individual and the employer. Should the employer find out and hold that against the institution that you're from, then that would, in my opinion, raise some concerns about the employer. However If this intern continues to act, or do things that might reflect poorly on the institution and by extension yourself, then of course it may be worth considering a conversation with someone from your institution.