I think the reason it's true is because without humility you will never ask for the grace from God to purify you, and without that grace - whether a Christian or not - there's no hope you will be purified. I always say, no one can be holy without the Holy Spirit, and His manifest Presence is not a given. It is granted by grace.
"Grace from God to purify you?", I'm not sure I'm familiar with that concept, can you please explain, I would like to know more