It is as reliable a source as we have (one of the authors is a respected historian, the other had an unprecedented and no-longer-available opportunity to read in the actual KGB archives for a while).

However, the book does rightly emphasize a challenge of interpreting these sources: KGB bureaucracy had incentives to inflate their ties to important people, so we have to be careful how much we trust even their internal record-keeping. For instance, there are a few comments in the archives they saw about Robert Oppenheimer being a possible source, but they're contradicted or unsubstantiated elsewhere. The basic historical consensus is that Oppenheimer was not working with the KGB at any point, yet it's easy for someone wanting a splashy headline to use the unusual comment as "proof" that he was.

There's a deeper epistemology question in us having to rely on this book's reliance upon sources that are no longer available (at least until Putin dies and IF someone more open takes over afterwards). Most historical work is premised on the historian acting in good faith, with the assurance that someone else can follow footnotes back to the original sources and see for himself. That's obviously not possible for now-locked-down sources. It's no reason to disbelieve the book, but it puts it on trickier ground, and underlines the impermanent nature of historical 'truth.' (Few historians these days would claim their history is True in a final sense, but lots of lay people seem to think history is objective facts arrayed in textbooks)