I am not sure what forum to use...

I am thinking of buying a website, is there any way to verify traffic independently?

Yes they can show you screen captures and all that but those can be easily faked. What's the best way to verify traffic?

(i have done some searches on here and google, and didn't find anything about this subject)

Thanks

Only stats can verify the true traffic ranking, but there are a few websites which you can somewhat gauge the popularity of the websites:

http://www.alexa.com (shows traffic popularity)
http://www.marketleap.com (shows link popularity)
http://inventory.overture.com/d/searchinventory/suggestion/
(enter key words to see how many type ins it should receive, eg web hosting talk, domain forum, etc...)

While these cannot guarantee traffic rankings, it will give you some additional info. I hope it helps.

Maybe you can ask them to install 3rd party counter, like stats4all etc.
It might give you the true stats

You really need a 3rd party stat program. You can sometimes use Webalizer, which comes with most control panels.

I like AXS Tracking (http://www.xav.com/scripts/axs/)

If you want to judge how well they are linked through seach engines Link Popularity (http://www.widexl.com/remote/link-popularity/index.html) can show you.