I look at copyright violations to be similar to breaking into your neighbor's (i.e. the copyright owner) house, using their kitchen to bake cookies, and then going back home to share the cookies with everyone and telling the neighbor not to worry because you're not going to earn a profit off of them. Some copyright owners are pretty laid back about it, some look at it as free promotion, but others have asked YouTube to block the content.
The best way would be to get direct permission from CBS to post the clip. I've asked permission to play songs - sometimes it takes a week to get a reply, other times it takes months to get a reply, sometimes I get no reply and need to send another email. If the video becomes blocked when you upload it with permission, you can then dispute the claim saying you have valid permission to upload the clip.
Laws vary by country, but in the United States there is the fair use law that a lot of people argue with their YouTube videos. However, the only person who can really decide what is "fair use" is a judge. If you made a video as more a "news broadcast" video, or an educational video of some sort with short clips, CBS may potentially see it as fair use and release a claim. The ball is essentially in their court to do so, as there isn't a YouTube judge to look at all of the fair use copyright disputes. I would argue that the majority of fair use claims that I've seen in YouTube video descriptions do not look like valid claims to me (but I'm not a judge...), so what could be considered legal/illegal in the public's view may have become a bit distorted.
But it sounds to me like you want to post a direct clip, so I would try to get permission. You don't know what they will say if you haven't tried. =) It's worth it to find out because copyright violations can come with heavy consequences.