When you use proprietary software, continued access to your data is generally dependent on your institution continuing to buy/lease/whatever. If you stop paying, your data goes away.
With Moodle (or other free software) you'll always have access to your data. Even if the open source project gets abandoned (not that that's likely with Moodle), you still have the source code, so you can always get to your data.
Ask them if they'd rent a physical filing cabinet with a proviso that if you stop paying rent, the rental company will destroy all your files.
Also, it's possible to add modifications to free software so that you can generate custom reports and analyses. While some proprietary software has a published API, it's not quite the same as being able to change ANYTHING.