Yes, I believe it is true (and so, incidentally, did my wife, Ruth, who often quoted this statement). But we also may be surprised when we get to heaven to discover who isn't there!
Why is this? The reason is because of a very simple but profound truth: Our salvation does not depend on us and our good works, but solely on God's grace to us in Jesus Christ. No matter how good we are, we will never be good enough to win our admission into heaven. God is absolutely pure and holy, and even one sin -- just one -- would be enough to keep us out of heaven. That's why even someone we think of as a very good person may not end up in heaven after all.
But God in His mercy and grace has provided another way for us to be saved -- and that way is Jesus. He was without sin, but on the cross all our sins were transferred to Him, and He died in our place. Now we can be cleansed of our sins and made ready for heaven, by trusting Him for our salvation. The two men who were crucified with Jesus had sinned greatly -- but one repented, and Jesus welcomed him into heaven in spite of his sin (see Luke 23:40-43).
Who are you trusting for your salvation -- yourself or Jesus? Make sure, by repenting of your sins and trusting Christ alone for your salvation. The Bible says, "For it is by grace you have been saved, through faith...not by works, so that no one can boast" (Ephesians 2:8-9).