It's the responsibility of the media to get it right.
It's not the responsibility of the Administration to prove them wrong. These people have important work to do for the American people -- instead of just making up stories to call attention to their imagined audience and ruthless ambitions to get to the top in the news/show business.
Every two-bit media wannabe thinks the President ought to seat them in the first row at the White House press conference and give them the first and last questions and as many as they want in between, without smirking and commenting, "Your wig is on crooked."