Although this is a health agency, it does not sound particularly healthy. This incident points to an organization with questionable understanding of the importance of treating people honestly and with respect and trust. Unless the agency is trying to increase ill will and negative publicity, there is no reason to treat applicants this poorly.
On the one hand, it is easy to rationalize that you are better off not working there, and it is better to learn this now rather than after being hired. However, the interview went well, you were supposed to go through the profiling system, and then you received the generic rejection letter mailed on the day you were interviewed. Something does not make sense.
You have nothing to lose by calling the vice president who interviewed you and indicating that you are confused by what happened. It is possible that a mistake was made, although it is more likely that the organization prevented you from making a mistake.
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