There are no simple solutions to a problem this complex as human trust.
But I really do not see, how I can I trust humans more, if it would be illegal to say true things about the past.
Truth may never be hidden, if you want real trust. And there need to be more consequences of lying.
And people should accept, that people change. If someone was stupid in their teenage years 10 years ago, then most can actually assume, that they changed a bit.
But if someone was lying and stealing 20 years ago and is caught doing it again yesterday, I will probably also not trust this guy in 2 years, unless he can convincingly explain why and how he changed.
The problem to be solved here is not the liability owed by the reporter of the truth, but rather the way in which our reptilian brains fail to balance that truth against an undoubtedly bigger picture.
Nicely contrasts with all the news about the omnipresent license plate scanners - it's just pointless, don't take the risk, arrest them at your leisure.