Could you be more specific when you say "billing info" (the rate or the total cost?). Just to ensure you are not missing something else - however I think you're talking about...
a bug or lack of good design that users can see task cost and through that extrapolate an hourly billing rate. The permission does shut off the RATE but there is nothing to hide the COST. If your users can do basic math then they can figure out the rate.
This is an issue that we would appreciate you voicing your opinion on via the support and greenhouse channels.