I'm guessing that criminals move in a little different circles than most people and it's their perception of "an average member of the community" that may be skewed rather than perception of self.
The ethics of crime are a complex subject, and while convicts' own views on the subject are generally self-serving there are shades of grey all over. For example, I knew a bar owner who murdered a heroin dealer, because one of the bar owner's friends OD'ed and died. So he waited until the heroin dealer went into the restroom at the bar one night, then followed him in and shot him dead.
That's pretty cold-blooded (from a legal standpoint, advance planning like that is considered far worse than shooting someone in the heat of a dispute), but then it seems morally mild compared to murdering someone for personal gain. I can't find it now, but there was a really fascinating article posted here a year or so ago about an undercover cop whose specialty is pretending to be a hitman, and the people who attempt to hire his services. Maybe someone else will remember enough detail to turn it up in a search.
Another good example of this dynamic can be seen with alcoholics (whichever stage of alcoholism they might be in). I read recently that apparently about 30% of the US population does not drink at all, and about 10% are outliers (10+ drinks per day!). http://kottke.org/14/10/the-united-states-of-alcoholism.
Having been a non-drinker for most of my life, and a heavy drinker for part of my life, in both cases I felt I was (mostly) 'average'.
Of course, what I failed to take into account was that in my non-drinking period I was part of a community of non-drinkers, and I barely interacted with those who drink a lot, whereas in my drinking period I didn't interact with the 'boring lot' who don't drink and leave parties at such early times as 12 PM.
Another example of this is sexuality. I spent a significant period of of my life practicing abstinence (conservative christian), and a more recent period in an environment where casual sex was the norm. I always thought that this more recent period was the actual 'normal', until I decided to look up 'actual' averages. I thought having a sexual partner count in the double-digits was pretty normal, but apparently here in Holland the average amount of partners is around 6, and the median is lower than that.
My problem is with the word "rather." It can be any degree of either in combination.
Perhaps generation 1 of criminals committed crimes out of perceived necessity, but did not believe themselves to be acting morally. They failed to stress this to their children however, perhaps due to some sense of pride, and the second generation is then raised to believe that crime is normal. This second generation, unlike the first, could have an inaccurate sense of what "normal" morality is.