Awstats would use recursive nameserver configured for a machine where you're running log analysis.
But resolution of IP addresses (called "reverse DNS") is something that often mistreated by IP-block owners.
If you think you can do better job resolving addresses you might disable AWStats DNS lookups and provide pre-processed logs, where IPs replaced to some kind of strings you generated...
I'm not user of AWStats, some info I found might be outdated:
- http://awstats.sourceforge.net/docs/awstats_faq.html#DNS
- see also example of program that does resolution, logresolvemerge