Just to clarify, the "Standard YouTube license" found in YouTube's ToS basically grants YouTube the permission to serve the video to anyone who asks to see it on YouTube.com or through an approved portal like an embedded player or mobile app (you may restrict the work's playback in certain markets, or prevent certain non-core uses, such as embedding, including in a playlist, listing in search results, etc). You, as the uploader of an original video, retain all other rights to the work including the right to prevent anyone else from using it in a derivative work, including a TV show.
Now, you may, and many do, give your express permission to the producers of a TV show to use the video in their own show. This is the honest and upfront way for the producers of the show to get the needed clearance, and it's done quite simply by sending the video's uploader a private message asking them for their permisison. If they want to use it badly enough, they'll pay you, but my guess is that >95% of the videos shows were shown without any financial compensation paid out; there's a lot of puke on the Internet, so Daniel Tosh doesn't ever have to look very far to find enough people willing to let him show their videos.
Now, the question is, what happens if they did't ask, or if you say no and they show it anyway?
Unfortunately, patent law is subject in most cases to the Golden Rule: Whomever has the gold makes the rules. In this case, the TV networks such as Viacom (MTV - Ridiculousness, ComCent - Tosh.O) and NBC Universal (E! - The Soup, G4 - Web Soup) have armies of legal staff for the sole purpose of representing the network in copyright cases, whether as plaintiff or defendant. The networks can and do take the stance that what they're doing is "parody", which is protected under the First Amendment and thus exempt from copyright law as "fair use".
The short version; while you may indeed own the copyright, free and clear, there is a limitation on your right to prevent derivative use of the work for the purpose of criticism, ridicule or satire. Such uses constitute "parody". This is, for instance, how Weird Al does his stuff (though he generally asks permission, and until relatively recently it was considered a great honor to most artists to have him parody their song). There is no line in the sand here, where on one side it's protected parody and on the other side it's copyright infringement. There is a legal test, but each allegation is decided case-by-case; it's a real can o' worms. Virtually all of these viral video shows air a piece of a clip and make a humorous statement ridiculing the person/people in it; that's parody, in the producers' eyes. So far, nobody has been willing to test this claim in court.
It's somewhat ironic that in 2007, Viacom filed suit against YouTube's owner Google alleging massive copyright infringement due to its users uploading Viacom's content, including clips of The Daily Show (which uses news broadcast footage under similar "parody" doctrine). Most of the "viral video" shows started up after that (Tosh.O and Web Soup in 2009, Ridiculousness in 2011).