From CNN which was quoting the original New York Times story:
The New York Times had reported: "When Mr. Trump is not watching television in his bathrobe or on his phone reaching out to old campaign hands and advisers, he will sometimes set off to explore the unfamiliar surroundings of his new home."
Later in the CNN article:
"I don't think the President wears a bathrobe, and definitely doesn't own one," he said.
Which CNN characterized
press secretary Sean Spicer said Monday the reporters got their facts wrong -- including the eye-catching detail that Trump watches TV in his bathrobe.
The idea is that details like "watching television in his bathrobe" make it sound like the writer knows these details. If the writer falsified those details, what other details are they falsifying? This is of particular concern in that many of the stories involve allegations made by anonymous sources. As per Spicer, apparently the Times made up this detail. How to know that they did not similarly make up other details? E.g. the anonymous source.
Donald Trump presumably knows whether or not he currently owns a bathrobe and whether he watches television while wearing it. He can evaluate that particular, objective fact directly. Photos of him wearing a bathrobe from thirty or forty years ago don't change that. They don't indicate that he ever owned a bathrobe (he could have borrowed one for that shoot) much less that he currently does. And they don't indicate that he wears a bathrobe in any space where there's a television.