Well, I wasn't talking about some hermit fully devoted to his own self without impact on others.

I was talking about someone pursing his own interests ahead of everything else - who would e.g. lie if it benefits him, steel, backstab, and so on.

This man might be an "whole and undivided" jerk, but he lacks integrity - that is, an actual good moral character.

So, "whole and undivided" is not what people mean when they say "this person has integrity". They mean that he is a "man of his word", has honor, is not two-faced, and so on.