I think exactly like you're thinking it does

Though God knows the intent of our hearts, and His Grace if sufficient, thank Him so much.
Christians are prone to vanity and sin too of course - all the more we need our Saviour. When we read the accounts of so many people the Lord used to Glorify them, we see they all were huge sinners, just like we all are. Moses killed someone, Paul in the New Testament used to persecute Christians also. David, a man after Gods own heart, committed adultery. That doesn't make sin ok, we reap what we sow, but that's the whole reason Jesus Christ came - for the sins of the world.
Conviction comes when someone truly believes God's Word is true, and so when verses like you posted hopefully will guide us, convict us, lead the Christian out of those things we do wrong for "self glory". Sometimes it takes longer for each one than another.
I can't tell you how many times a day I sin. Even in my thought process. The more I learn from His Word, the more I know I need help and guidance away from any "self righteousness", away from any "pride", away from so many things, but instead to love.
His Word is likened to a double edged Sword and also the "Sword of the Spirit". Truly amazing, and also helps us instead of hurting us. Even though our "flesh" will sometimes kick against Him.
Hebrews 4:12
For the word of God is quick, and powerful, and sharper than any twoedged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart.
Heb 4:12 is an amazing verse.
Ephesians 6
11Put on the whole armour of God, that ye may be able to stand against the wiles of the devil.
12For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places.
13Wherefore take unto you the whole armour of God, that ye may be able to withstand in the evil day, and having done all, to stand.
14Stand therefore, having your loins girt about with truth, and having on the breastplate of righteousness;
15And your feet shod with the preparation of the gospel of peace;
16Above all, taking the shield of faith, wherewith ye shall be able to quench all the fiery darts of the wicked.
17And take the helmet of salvation, and the sword of the Spirit, which is the word of God: