Generic Business Nonsense
I figure it might be helpful to view tardis like a business, albeit a business which aims neither to make any more, nor to raise a particularly large amount of money. The purpose of a business is to create value for the customer by providing a solution to our customer's problem.
One way to view tardis is with students and societies as our customers and admins being "employees" who keep tardis running in order to provide them with a cost-effective solution to their website/email/etc needs. However, Informatics doesn't care about other students or societies. They care about inf students, i.e. the admins. So we need to turn it on it's head.
So, the admins are tardis' customers, and their problem is that they're going to leave uni with a decent degree, but next to no practical experience or useful connections, both of which are pretty handy when it comes to looking for a good job these days. Tardis solves this problem by giving them an opportunity to work with a team of like-minded individuals to maintain a computing system which has a large userbase, providing them with the practical experience of working with a large-scale system and implementing and maintaining numerous popular services for the users. This allows these students to become better skilled, more experienced and fundamentally better prepared for the workplace.
Informatics are effectively investors in tardis, so we need to align ourselves with their goals - having a great reputation as a university by producing top-notch graduates, so that more graduates want to come to Edinburgh, so that their research can get funded. If we help them to see why we make their students better, they should be happy to give us space.