EZRA – I have two responses to your take on this: the practical and the legal.
Practically speaking, you apparently feel that once a member of the audience at a graduation starts a prayer that is, assumably, acceptable to the majority of the audience, someone on behalf of the school should . . . What? Shout him down? Forcibly make him stop reciting the Lord’s prayer? I don’t see how this would improve the overall ceremony; indeed, you might find the graduation disintegrating into a melee of various factions shouting at each other. So, as a school official, though you might not have expected or condoned the prayer, you probably would feel that the greater part of valor is to just let it pass and get on with the graduation.
Legally, the government cannot establish or promote religion. This does not mean they have any obligation to stop the establishment or promotion of religion by private citizens – indeed to the contrary, they can’t do that, either. If an individual decides to say a prayer at a graduation, be s/he the valedictorian or a member of the audience, the government has no duty to shut that person up. The prohibition on the establishment of religion applies expressly and ONLY to the government itself. For this reason, your question of whether the individual quoted in the article “intended to comply with the constitution” is an irrelevant one; the constitutional prohibition in question does not apply to private citizens, so what she did or did not do, and her motivations, are under no circumstances unconstitutional. You infer that the school somehow had prior notice of the intention to say the prayer and that it “intended” the moment of silence to be a moment of spoken prayer. I read nothing in the article that would support this inference. But even if the school HAD known about the prayer, as I said above, it had no constitutional obligation to stop it.