No, it means he probably wouldn't push an old lady to her death in the first place.
But if he did, he would be ashamed of his sin, repent of his sin, ask God to forgive his sin, and ultimately, he would know even that terrible sin has been covered by Christ on the cross.
That's what Scripture says, and I believe it.
"But God, who is rich in mercy, for his great love wherewith he loved us,
Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;)
And hath raised us up together, and made us sit together in heavenly places in Christ Jesus:
That in the ages to come he might shew the exceeding riches of his grace in his kindness toward us through Christ Jesus.
For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
Not of works, lest any man should boast.
For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them." -- Ephesians 2:4-10
I know -- I am Catholic.
The short answer is yes.
It's cute how these discussions can be so one sided. RC's are always saying we fail to understand the depth of the meaning in their beliefs. Yet at every turn we see RC's misquote responses or come up with farcical situations.