I assume that the youtube moderators watch as many videos as possible during the time they're working their to see if any videos violate there Terms of Service but it would be really impossible for googles employees to watch every video that is uploaded to youtube since millions of new videos are being uploaded to youtube every single day.
And there's already billions upon billions upon billions of videos on the youtube website already.
So while they do monitor some videos they're not able to watch every video on their website.