The person in charge of someone else’s funds sometimes has a special status. The Shulchan Aruch (Choshen Mishpat 37:9 and 290:12, respectively) says that a gizbar (person in charge of tzedaka funds) and an appotropus (legal guardian of orphans) can testify on behalf of the funds they handle. Similarly they are not personally sides to the dispute, as far as their responsibilities before the court are concerned. However, the status of a person or group of people who together start an NPO (non-profit organization) does not allow for these halachot. Rather, they have the status of owners or parties to the dispute. This is not to take away from their philanthropic intentions; it is just that their level of involvement is higher.
The Maharam Shick (CM 18-19) says that the public and its representatives have no say as to the internal running of independent organizations of Torah and chesed. Based on this, we have ruled that beit din cannot force a yeshiva to accept a specific student. It seems that the determining factor in borderline cases is whether the person can be removed from his post without any specific wrongdoing. This may be supported by the following set of sources. The gemara (Bava Batra 46b) says that a sharecropper can testify about the ownership of the field he works on because its ownership does not directly affect him. The Nimukei Yosef (ad loc.) says that this is not so in regard to the type of sharecropper who cannot be removed from the field. In other words, not being able to be removed creates a special relationship that makes him unable to testify.
There is another concept that impacts on the director’s status. The gemara (Megilla 26a) says that although shuls that are attended by an open-ended segment of the population cannot be sold, the shul in Mata Machsaya, where people donated toward it with the intention that matters were at Rav Ashi’s discretion, could be sold by him. Similarly, when an individual founded and runs an NPO as its clear leader, he has a halachic status as its leader.
There is yet another reason that the director is required to adjudicate as a party. The Torah, in describing the litigants (Devarim 19:17), talks of "the people who have the dispute." Thus, even if they would not be considered like actual owners, such as in relation to monetary ownership, if their regular involvement in the operations makes them the de facto disputants, that is the way they will be halachically viewed.
Regarding whether the laws of following the local practice apply, although the status of tzedaka organizations is somewhat different than standard, this does not apply to the organization involved in this case. Since most of its budget comes from funds from government agencies, the same norms of behavior that apply to other such institutions, including universities, apply to them.