I do not think it means what you think it does.

100% of the credit for this goes to Breda. 

The punch line, like for all good jokes, is near the end. 

'Open to the Public by Invitation Only.' 

Now, as a disclaimer, I can't find what is officially in the White House Itinerary for the speech.  Another article says 'Public Attendance is by Invitation Only', which is still a pretty loose interpretation of 'Public'.

One can only HOPE that the Administration realizes it is CHANGING the definition of the word 'Public'.