Hard to say without some really good close-ups of the fracture face but it would appear as though the threaded adjusting rod failed in fatigue rather than a single cycle overload. This would lead me to believe that either there was a flaw in the threaded rod itself. Fine thread vs coarse thread would not have made a blind bit of difference, the grade of the steel in the threaded rod definitely would have.
I'm also at a bit of a loss to explain how everything is so clean. Cranes that use clutches & brakes are not normally like that. How long ago was the brake band fitted, and how does that tie up with the apparent amount of wear on the friction material..? Because the photos are not totally clear I'm going to hazard a guess here, judging by the amount of welding around the lug, that this may have been a modification of the adjuster designed to extend the life of the brake shoes for a few more hours when the original adjuster got to the end of its travel.
Incorrect installation if it was recently installed could also have been a factor.