But that's not what it says, so it's not appropriate.

"We keep the data that you store with us confidential. Our staff will not look at it unless you specifically ask us to investigate a specific issue. Other than legal requirements (e.g. a valid subpoena) we won't share it with anyone unless you've identified them to us as part of your team or otherwise authorized to see your data."

You should always say what you mean in contracts.