That is a very accurate statement, but perhaps misunderstood. People who do not believe in God can and do commit moral acts, and are more prone to do so in a society that is influenced by the "salt and light" of believers who carry the presence of the Holy Spirit. But this doesn't mean that unbelievers are therefore moral or that acting morally is their default position. Paul clearly teaches that unbelievers are slaves to sin and that Sin is their default position from which they might choose to do right in certain circumstances. On the other hand, believers become slaves to God so that Obedience becomes the default standard from which a believer might (and often does) choose to sin in given circumstances.
The writer's point is clear and accurate: Apart from belief in God and the restraining influence of the Holy Spirit, there is no objective and enduring standard of behavior, and a Godless society will eventually collapse into every kind of anarchy, suffering and destruction. That is the reality of the ugly sin that Jesus dies and rose again to save us from.
dies = died