Economic Data - Who knows what when?

The Labor Department releases weekly 1st time unemployment claim numbers every Thursday at 5:30 AM and monthly unemployment data at 5:30 AM once a month. Technically, I suppose, they release the data a bit earlier, but advise media outlets that they cannot release it until 5:30. Anyway, how close to the vest does the Labor Department keep this data? I find it hard to believe that the White House doesn’t have access to it at least the day before. Anyone know for sure?