I was thinking along the lines of Kyron asking to go with her, her agreeing for whatever reason and then something happening after they left the grounds. There would not have had to be a scene at/in the school.
But then it does not explain why she would not have stopped long enough to tell his teacher, hey, he's coming with me...
I think that if TMH did this, it may have gone down this way:
TMH and Kyron go into the school together. They drop his jacket and backpack off in his classroom, then TMH takes the famous picture of him.
Right after she takes that picture, she realises Kyron forgot something in the truck. They head out to the truck together. While they are standing by the truck, TMH loses her temper, shakes Kyron and accidentally kills him.
She panics because she knows she should not have been shaking him, stuffs him into the truck and leaves.
Later, when asked about her movements that day, she reverses the two events. She says that first they went back out to the truck together, then came back in and she took the picture (with witnesses), then they walked around together.
Even if they were seen going out to the truck together, that would mean nothing because it is accounted for in her timeline. I doubt anyone who might have seen then consulted their watch to check the time. The time discrepancy would only be about 10 minutes.
Again, this is only speculation. It is one way this could have happened but I have no way of knowing that this is in reality what happened.
