There is no such thing as an absolute waiver of rights. This includes especially the right to appeal a reduced charge and sentence (you cannot waive Constitutional rights, statutes of limitations, incompetence of your own counsel, or prosecutorial misconduct - these are only some of the most common).
When the prosecutor says this he knows he's lying.
Even worse: he doesn't - lots of idiots out there with law degrees.

In general, if you're at risk (possible tortfeasor), it's better to construct an elaborate waiver with as many provisions and acknowledgments as possible, because it has the effect of frightening the future plaintiff's attorney into accepting less money.
It should be executed by a Notary as an "acknowledgement" (not sworn, not an oath, not an affidavit) similar to a conveyance of real property or a contract.