Are you talking about just the domains or the embeded content too? Meaning do you only care about requests to http://www.facebook.com or do you wish to include the embded content like static.ak.fbcdn.net?
Without enabeling page views, it can be very difficult to get the embeded content. What's the end goal?
First, there is no tracking of browse time by site. Browsetime is only tracked per user and client IP address. You can say that user jdoe spent 20 minutes browsing the web, but you cannot say that 10 minutes were spent on facebook and 10 minutes on cnn, etc. Please disregard that you can actually have browsetime on the report next to the site name. This is really a side affect of how data is stored in the database.
However, with page views enabled, browse time by site should be fairly accurate since the embeded content is rolled into the original request. The page view feature throws out the urls like ad.doubleclick.com, and media.sitex.com,
I'm aware you don't have page views enabled since we spoke about it last week over the phone. You need to make a choice about the content you want to have available. If you enable the page views, your database size will decrease significantly, but you loose the ability to run reports on requests for embeded content like stylesheets, java scripts, etc. But the browse time by site, although not tracked by site, would be fairly accurate.