Personally, I blame the Grissom for the additional damage.
Hear me out on this- I read Vonda McIntyre's novelization, and it makes it clear that all the various galactic governments became aware of Genesis after an entire nebula vanished. It isn't much of a stretch to think that they were well aware of two Federation ships taking potshots at each other.
With that in mind, the Federation sent the nearest ship (the Grissom) to investigate. With the Enterprise limping along to home base, ol' Esteban probably figured it was a free-for-all and thought: "Hey, if the great Admiral James T. Kirk thinks he's going to put one over ME, he's in for a big shock! Helm, raise shields and HIT 'EM WITH EVERYTHING WE GOT!"
Luckily, cooler heads prevailed, but not before Grissom got in a few licks.
This would have given us this opening scene in the movie:
In the original script, there would have been an additional line of dialogue when Kirk mentions the Grissom on the way to the Genesis planet: "Will she join us... or fire on us...
like last time?"
Real-world explanation: Harve Bennett wanted a recurring joke with Kirk yelling someone's name in every film, but Shatner liked the above dialogue so much that he took it for himself for later in the film. Necessary changes were made, and we ended up with what we got.
Side note: Please do not take this post seriously.