Unless you are using a service like tarsnap, your admins can and will peek at your data. If you use a service like tarsnap, and you lose your password, your data is deader than disco. Pick one - security, or an admin who can save your account.
And while it's theoretically possible to develop a rich web app without seeing user data, it just doesn't happen. You need realistic data to do testing. The most realistic data you can possibly get is your user's data. Guess what 99.999% of websites use for testing?
If you have sensitive information, use good encryption. Better still do what the professionals (i.e. the government) do, and leave it on an internal-network only computer, in a steel reinforced room. If you're paranoid, lock the hard drives in a safe when you leave the room. And use encryption.
But don't make a fuss when the admin peeks at your data, in a semi-random way. If they are stalking you specifically, or leak any damaging information, that's another matter. But if you just don't trust them, don't give them your data.