They know how the press works though. There's a huge amount of attention being paid to this launch, and journalists will be racing to report it ASAP. If they announce immediately that the centre core has been destroyed, the headlines around the world are going to be "SPACEX LAUNCHES CAR BUT LOSES SPACECRAFT", and the failure, however partial, will be a central plank of the story.

If they delay the core announcement by a couple of hours or so, the headlines are all "SPACEX SENDS CAR TO MARS", with a minor note appended later to say, "A SpaceX spokesperson later confirmed the landing of the spacecraft's central core did not succeed and it has been lost." Like it or not, issues of timing like this makes a big difference to how the exact same events are reported and perceived.