RE-call for opportunity?

Interesting question...if all the information you suggest is true. We must, however, be careful not to make assumptions. As someone who went through the applications and interview process, there are many similarly title jobs that are indeed treated separately. There are really only three possibilities:

Possibility 1: the position is the identical position and slot you applied to fill; Possibility 2: The position is identical in title, but actually there are multiple slots; or Possibility 3: It is a different position (slightly or otherwise).

Let's examine all three.

If it is truly Possibility 1, then the company has lied to you. However, you do not, nor will you ever, have enough information to prove it (asymmetrical information = impenetrable plausible deniability). And even if you could prove it, you aren't going to be able to force their hand to either admit their lie (possible liability) or allow you to apply again. So, possibility 1 is not something you can determine- and if you could, it wouldn't be very helpful to you. If possibility 2 or 3 is true, you can simply re-apply. My suggestion- apply for the position listed at your friend's school's site- handle the situation as if you were applying for a different position. Don't mention how you found out (unless prompted- and even then, your response should be 'school website'). Don't call (if you don't have to). Apply just like you did the first time. I will not comment on submitting multiple applications to the same firm within the one hiring cycle.