If there is fake news out about someone in the Trump administration, Trump would not let it rest.
Exactly. Trump’s tweets are not time consuming. That’s part of why he does it—because it’s a quick and efficient way of bypassing the media and speaking directly to his supporters.
There is no cogent or rational reason Trump wouldn’t slap the WaPo around if they’d printed yet another fake news story. Not only does Trump appear to enjoy mocking WaPo, but his correction-tweets also serve to undermine the reputation and perceived reliability of his critics. Trump would not miss another big opportunity to further denigrate/embarrass his most rabid detractors.