Not sure about this - seems like Elon's personal meddling has shown that Starlink is not reliable for military purposes. Military would have to have complete ownership/control
The US doesn't have any current plans for military version of Starlink. They have a pretty extensive satellite system. Starshield is SpaceX project to use Starlink technology for military.
The US Space Development Agency, focused on missile defense, is working with SpaceX on tracking and communications constellations. But the communications is using laser links for in-space communications. Military Starlink is possible but not proposed yet.
Walter Isaacson, the book's author, gave a long-form interview recently on The Lex Fridman podcast. In case you'd like to form your own opinion about the book's legitimacy, its writing/Musk-supported research is substantially discussed:
Musk has since stated that the satellites were always disabled in the Crimea, as per requirements of US sanctions, and that SpaceX would have turned things on if requested by the American government, but no such request was made. Is he lying?
>A senior Ukrainian official has accused Elon Musk of “committing evil” after a new biography revealed details about how the business magnate ordered his Starlink satellite communications network to be turned off near the Crimean coast last year to hobble a Ukrainian drone attack on Russian warships.