I'm convicted of committing a crime that I did not commit. During the legal process I am questioned and, because I have no right to remain silent, I must tell the investigators/prosecution/whomever that I did not do it (truth). That denial is then used against me during sentencing because I 'lied' and thus I receive a harsh sentence.
In a world in which I have the right to remain silent, I say nothing during the legal process. While I'm still incorrectly found guilty, I have no denial on which to pin a lie and therefore am sentenced more lightly.