I certainly understand why parole boards have required these admissions. If someone has committed a crime but will take no responsibility for it, that certainly does not bode well for their future behavior.
The problem is that the justice system is not perfect, and occasionally convicts an innocent person. It's not right to demand that someone admit to a crime they actually didn't commit, and to deny them parole until they do.
Accordingly I submit that the only consideration for parole should be the convict's behavior while incarcerated.
Occasionally? Given the 4% rate of false conviction for death penalty defendents (http://www.pnas.org/content/111/20/7230.abstract) and the fact that 97% percent of criminal cases dealt with in the U.S. don't even go to trial, it's far more than occasionally. Often. Quite often.
The rate of conviction in Hypothetica is 100% for all crimes. If you're charged, you get convicted.
What percentage of the convicted were convicted falsely?
Which pretty much leaves only the left of center and if the last elections are any indicator, we'll be lucky not to get declared criminal by all of the above.