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.