What I am saying is that I am not sure discussing the appointment is appropriate, since it was not reported by LE or the parents.
If it is ok to discuss it based on the unverified account of the SMs friend, then, what she supposedly said was that the SM gave the teacher a form
the day before (the 3rd) (when there was no chaos at the school) and said Kyron had an appointment on the 11th, and that she needed the paperwork back before then.
IF we are to take this friend's statement as fact, then the appointment has no relevance at all. The teacher should not have thought Kyron had an appointment the next day. I would in fact guess that the teacher had not been able to immediately return the paperwork the same day, and therefore could not really have thought the SM took Kyron to an appointment without the needed paperwork.
On the other hand, it is entirely possible (if it is true) that the teacher just plain didn't pay any attention to the SM asking for the paperwork, only heard the word 'Friday' (instead of Friday the 11th), and ASSUMED he had an appointment the next day, none of which SM could have been responsible for, as far as misunderstanding.
If the other second-hand story is to be believed, that SM yelled across a crowded gym that he had an appointment the next week, you'd have to believe that at some point they were in a crowded gym at some point, which none of the established reports show as true.
If I am crossing any TOS, let me know.
I think posters are just trying to discuss the possibility that the reported appointment has relevance to Kyron's disappearance.