If you are Radically Honest then you can't keep a secret. Wouldn't that make you less trustworthy and thus lower incentives for people to be honest with you?
You can presumably say 'I can't tell you that', which suffices in many but not all circumstances.
Interesting point, J Thomas, there is often more than one truth that could be told. How would/should you choose which one to tell? The difference between Eliezer's "tell no lies" and Radical Honesty no longer seems so clear cut to me.