No the sad truth of dispensational arminianism is that they cannot even admit they are sinners. Jesus came into the world to save sinners not righteous people! The apostle Paul said he was the chief of sinners and are you better than him? The sweet little innocent baby who never hurt anyone is a child of sin and unless his parents place him under grace by their faith in Christ he will grow up and become assimilated into the world.
If Paul was the chiefest of sinners, as you seem to understand that text, then I'm a monkey's uncle. If you think your children are saved because you are, and your unsaved neighbor's children are damned, then you believe God is a respecter of persons. Children are not responsible for the sins of their fathers, and we are all saved individually.
I'm not sure where you get the idea that some cannot admit they WERE sinners. Check the tense....such were some of you. Do you hang onto the the title of sinner because you reject Christ's work on the cross, or what?