Yes, why not? The only reason I see not to tell the truth is that you're guilty according to the law; that then only seems morally justified if the law is unjust, in which case you should challenge the law IMO.
There are very good reasons to have something like our 5th amendment that apply to people who are indeed not guilty according to the law. It's not about telling lies, it's about not providing truthful information that can be used against you in ways designed to make you look guilty even when you are not.
The founders of our country who made sure we had a 5th amendment knew the importance of this -- they didn't put it in there to protect the guilty.
Or you're protecting legal secrets that protects other people. Like secrets about where somebody who is stalked is, crypto keys to security systems, etc... Or hobbies of family members that the rest of the family really do not approve of. And so on... Sometimes it just isn't justified to demand access to such information and punish the person of anything is left out or covered up. Sometimes demanding that the person tells the truth is worse than not to.
