Web site stats have always been problematic. For pretty much the entire time that web sites/servers started keeping statistics, there have been those trying to exploit them.
This blog, as an example, doesn't have that many real people per day visit it. And yet the blogger stats page says it gets 200+ hits a day. Most of this would be various spammer hits, bots that visit the page hoping that either a) you are silly enough to publish your referrers or b) that you will use the links left behind by the referrers. Bad news people, I am not EVER following those links.
Now for the actual sites, it gets interestingly really weird. My current host offers AW Stats. I also have my site set to use Google analytics. The two of them paint very different pictures. Some of that is to be expected. AW Stats has access to the log - the real hits to my site. While it tries hard, it does have a difficult time separating all the spiders/bots that visit the site from the real visitors. So it over estimates the number of people who visit.
But where the story gets really wild are the referral spam. There are basically two sets, those who target normal logs/stats and those who target your analytics.
I do understand why there are those who target normal logs. Some web sites publish their stats, you can find AW stats out there. So any referral spammer in those logs might get their links published with the stats. Since my stat page is private, it makes little difference to me. I wish that they'd stop but that's not likely to happen this decade.
I do not understand why anyone specially targets analytics. I've had sites with fake languages show up in the language area. I've had sites that I know don't link to mine show up as referrers. I've even had to block some sites that used my tracking code on their page and showed up as one of my "most hit" pages. To me, that's just weird.
In particular though, the referrers that show up in the AW stats are mostly different to those that show up in the analytic stats. There are a few that are in both and a few that are ACTUAL referrers to my site. For the most part, they are different.