The CBS AllAccess setup is a little different than the situation where local stations are streaming local news or news clips.
The stations that are offering news programs or clips are probably using a third party service that either records and host, or takes uploads and hosts the content. Some are available via LiveStream, while others use a standalone app.
I have no idea what kind of costs are involved, but it's probably not extremely cheap. They'll either have to try to recover costs with advertising (ITT Tech or DebtSucker commercials and the like), feel that the online stream makes up for the cost in some intangible way, or just not do it. Many choose Option C.
Roku Ultra (4660)
Apple TV (5th gen), TiVo
Roku boxes from every generation.
Apple TV (2nd, 3rd, 4th gen)