I believe that the following quotations, from the president of the USA’s largest atheist organization, the Freedom From Religion Foundation (FFRF), Dan Barker, and from the president of PATAS, the Philippine ATheism,Agnosticism, and Skepticism (Society), are helpful in illuminating Psalm 14’s statement:

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.

Dan Barker [Freedom From Religion Foundation president]: “Even if Jesus did exist, even if I agreed …100%–yep, [Christ] rose from the dead; yep, there’s a God; yep, I don’t deny any of that—does not mean that He’s my Lord.  If He did exist, I will go happily to Hell.  It would be worse of a hell for me to bow down before a Lord regardless of the legend and historicity issue.  Even if I agreed 100%, I would still reject that Being as the Lord of my life because I’m better than that. …Amen. … I cannot accept Jesus as Lord.  You’re much more free to live and enjoy your life unshackled from the demands than have some Lord of your life.  To me, I think that’s more important than all this historicity stuff which you heard me admit is a matter of probabilities  I might be wrong.  That still doesn’t mean that Jesus is Lord.  He’s not the Lord of my life. (Dan Barker-Thomas Ross debate, “The Old Testament is Mainly Fiction, not Fact”. 1 hr 48 min)