It's important to remember NASA consists of more than just Johnson and Kennedy (space centers). Each center focuses on certain areas that are important to NASA's overarching mission. Ames, actually, does a lot of computer science and software engineering research, so this makes sense to do here.
Additionally, NASA deals with a lot of data, for example from their earth-monitoring and climate science missions. There is a huge need for computing infrastructure, and a resource like this that can be shared across NASA centers is a great benefit to researchers across the agency.
Regarding sensitive information: the mindset at NASA (at least among the PHB's) is to be super paranoid about any possible data breaches. PR is extremely important to NASA, and if there were any major embarrassments due to data breach that could result in decreased funding, which as we all know is already incredibly tight. So, by providing services like this in-house, it's much easier for teams at other NASA centers to get access to the resources they need without jumping through hoops to get clearance. I will note that much of this feeling is a result of ITAR, so NASA's concerns are definitely well-grounded.