I have no doubt that Trump's hand chosen spokesman will stick to his story. However, it will take more than his word to convince anybody. Mueller's actual report is required for that.
Let's assume, Barr and Rosenstein aren't stupid. They both know the report will, in some form or other, see the light of day, and that they will be raked over coals if they materially misrepresented it.
Let's further assume that Mueller is the by-the-book guy we've been told he is, who would respect and protect the Constitutional institutions that hold the Republic together. And that means, he, Mueller, will not throw the Republic into a Constitutional crisis by requesting Trump be indicted, while that, under current guidelines, cannot happen. That was to be expected.
So, he writes a report showing there were numerous contacts between Russians and the Trump campaign, but stops just short of finding a criminal conspiracy. He further lays out a pattern of behavior that may seem like obstruction, but withholds judgment on that.
What to do now? Mueller would insist, based on the evidence provided and further evidence unearthed during Congressional investigations, that the respective Constitutional institutions do their jobs, and refuses to do it for them. If, or so I believe Mueller's thinking goes, the Americans or their representatives want that sorry, mendacious, thoroughly corrupt excuse for a president gone, the institution to make it happen, Congress, should go to work. If they think what Trump and his campaign have done is acceptable, and want him to stay, it's not his, Mueller's, job to thwart that.
That is, I believe, where things stand right now. The work to reveal the extent of the Trumpsterfire is off to a good start, and the work to extinguish it has just begun.