I believe this does not affect green card holders. My understanding is that green card holders are entitled to enter the U.S. in a similar way that U.S. are entitled to enter the U.S.
I don't think anyone would expect this to affect green card holders, and if this isn't an outright fabrication, which frankly wouldn't surprise me at this point, I'm sure Trump will clarify the matter shortly. No one wants these policies to affect established, permanent residents.
Remember, this is a very hard transition and the teams are still in the process of exchanging. It's absolutely plausible that there are anti-Trump people in the government doing everything they can to throw a wrench in the works. The media has certainly made it clear that they're basically willing to self-immolate to try to stop Trump, and I think there are a lot of Obama-era workers of similar mind.
Reuters has edited the story linked above [0] to state that the spokeswoman had improperly stated the effect and that, per a "senior administration official", permanent residents will be allowed to enter the United States after a "routine rescreening". [Permanent residents, or "green card holders", are non-citizens who have been granted a permanent right to reside in the United States.]
As expected, this is just another case of the media heavily misrepresenting an action by Trump because they want to destroy him at any cost.
[0] See http://archive.is/JViXa for a snapshot of the Reuters article at Sun Jan 29 01:52:21 EST 2017. The old snapshot is accessible by clicking the "history" link on that page, or going directly to http://archive.is/ZwEBt .
Or it is the result of an amateurish group in power, which seem not to understand the consequences of their actions.
Source: http://www.cnn.com/2017/01/28/politics/donald-trump-travel-b...