What I'm thinking, is that Jameson's mom read the report that she left him on the dumpster, and assumed that when he fell through the hole, she and milo left him for dead.
If you notice, his pistol landed about 10 feet from where he did, so he crawled over to get it. In the scene right before he kills the mercy, you can see the hole he fell through framing the mercy's head, showing how far he moved. Since the basilisk came from behind him, it's unclear if Katie could have seen the basilisk or even heard any indication he was in trouble before it was too late, regardless of if she could have got a clean angle on it. Now as to why she wasn't keeping an eye on him, I think she thought "the guy broke his leg, he ain't going anywhere fast".
That's just my 2¢.
This is how I followed it,