This is pretty simple. This incident happened just as "American Sniper" was really taking off, and it seems clear that NBC was taking advantage of this 'interview' to, once again, trash the American soldier. Especially an American soldier that distinguished himself in "Bush's War". This has been done with varying effectiveness since "Full Metal Jacket", and has been a theme of the "News Business" since Vietnam. Portray any effective American soldier as a crazed killer, looking to "eat dead burnt bodies", as Arlo sang it.
This segment on Morning Joe was just a continuation of that thought. That it was completely without foundation was not a thought that crossed their minds. They didn't try to talk to anyone that actually knew Cris Kyle. No. They had their agenda and they ran with it. That's how it works in modern media, and any apology, written or on-air will be sandwiched between a commercial and a segment that people really want to see. If you were not looking for it, it will be very forgettable. If you took a poll of the viewers before and after the apology, you will find very little difference in the predominant opinion that Cris Kyle was a racist killer.
Mission accomplished.
Oops. Cris is spelled Chris. Sorry.