Le Monde and Al Jazeera are now reporting mutually consistent accounts of what transpired. It turns out that a rocket fired from well South of the hospital was intercepted by an Iron Dome anti-missile missile. The debri from the intercept explosion fell to ground in several locations, but the unexploded warhead of the rocket exploded on impact with the groung in the middle of the hospital's main courtyard.
This helps to explain one aspect of the NYT photo: the damage in the right foreground to the roof of one on the hospitals buildings. Around the collapse hole are smaller bits of debri. The piece that caused this hole should be closely investigated. It may well turn out to be part Israeli and part "non-Israeli".
So, the mutual finger point is "correct" but for the wrong reasons!