Doesn't sound arrogant to me either. It's a bit like saying "I tried to exceed my customers' expectations"... in fact, it means exactly that...

I don't read it that way at all. I read it that he tries to exceed people's expectations in his personal relations.

If it sounds "horribly arrogant", then I think that sounds horribly negative and judgemental.

It would be arrogant if it said "I treated people better than they deserved".

Not necessarily. As a small business owner, I aspire to this as well, if only because my experience has been "I expect my employers to get all they can out of my while paying me the bare minimum and treating me as poorly as I'll tolerate."

Granted, this is just my perspective, but that does suggest that this statement can mean various things depending on who you are and how you've been treated yourself.