"Isn't under sin"? Are you just going to make stuff up that has nothing to do with your claim? Paul wasn't "exaggerating" but he certainly wasn't contradicting Scripture as your "interpretation" insists. Have you ever bothered to go read "what is written" in Psalm 14 and Psalm 5:5-9 which Paul was quoting? It's the foolish...."their hearts" are being talked about...not all men.
It's the fool who has said in his heart there is no God. That does not mean all men are fools and don't believe in God. We know from reading Romans 1 and 2 that the things of God are clearly seen and understood by the created. It's why men are without excuse. Even the gentiles can do by nature the things contained in the law.
Psalm 14:1-5
The fool hath said in his heart, There is no God. They are corrupt, they have done abominable works, there is none that doeth good. The Lord looked down from heaven upon the children of men, to see if there were any that did understand, and seek God. They are all gone aside, they are all together become filthy: there is none that doeth good, no, not one. Have all the workers of iniquity no knowledge? who eat up my people as they eat bread, and call not upon the Lord. There were they in great fear: for God is in the generation of the righteous.
There has always been those who are righteous and just (not sin free - and that isn't what Paul is saying).
Why do you ignore Able, Noah and Lot? Mat 23:35 2 Pet 2:7,8
Gen. 6:9 These are the generations of Noah: Noah was a just man and perfect in his generations, and Noah walked with God.
Why do you ignore those who sought the Lord?
Gen. 4:26 And to Seth, to him also there was born a son; and he called his name Enos: then began men to call upon the name of the Lord.