Regarding lying....
If i am the type of person to commit a crime in the first place, then evidence is pointed to my involvement, of course i am going to lie my pants off to try to get out of paying for it. What have i got to lose, so then if i eventually plead guilty or "come clean" there is not going to be much more of a penalty for lying about my involvement (im not talking about lying in court), except that some people will call me a liar, but in comparison to what i am already going to endure or go through for comitting the crime - what is the big deal if pople call me a liar on top of that.
If i commited a crime, i would lie about doing it all the way until my sentence is announced, and even then i might lie and say i was unjustly accused, unless i was caught redhanded.