Montefiore had access for the first time to unsealed Soviet records he says were about Beria investigating the rumors, finding out to his shock they were probably true and covering it up again.

Did he publish the records? According to the reddit post:

[Montefiore] cites a statement by KGB head Serov that supposedly confirms the story but there is no actual reference to this document in the bibliography, nor an image of the document in question. The only direct quote from this source is: “J. V. Stalin started living together with her.” [i.e. in the same house as her parents]