So there's a good chance the club asked him, as captain, to support the manager, and arranged for him to speak to the media. But I still wouldn't expect the club to tell him exactly what to say (or for him to do so if told). It's also possible that Greer does actually believe in the manager.
He didn't have to say what he said though. He could have just said the players are responsible for missing all the chances they've had, and individual mistakes have cost them points, and said they were behind the manager etc. He certainly didn't need to say Sami was a better manager than Gus or...