Madame Maxime, headmistress of Beauxbatons, was naturally very different from Hagrid, the gamekeeper who lived on the edge of Hogwarts. Even though Pomona had never met her, she had heard a little about her.
Alchemy had always been Beauxbatons' strength, but Madame Maxime's accomplishments did not lie in academia. Rather, she had managed a school made up of students from many countries remarkably well. An international event like the Triwizard Tournament was novel to Hogwarts, but not to Beauxbatons.
She was like an elegant hostess, presiding over one salon after another where hosts and guests alike had a wonderful time. Though Hagrid seemed to Pomona like a kind-hearted giant, that did not mean he was acceptable as he was now. Being friends was one thing; being a boyfriend was another.
Pomona did not really approve of Albus's idea, but the Philosopher's Stone had already been destroyed, and it was unlikely that another could be made. If Beauxbatons insisted on demanding the Philosopher's Stone, or on witnessing its destruction, that was no longer possible.
If Hogwarts said the Philosopher's Stone had been destroyed, did that mean it really had been? Why could Hogwarts not have used its destruction as a pretext to pocket the Philosopher's Stone for itself?
There was no way to explain such a thing. Besides, Albus and Nicolas Flamel were close friends, and many of the things Albus possessed had been gifts from Nicolas Flamel. Were they really going to demand back gifts they had already given?
It was a good way to solve the "trouble": send Hagrid out to distract Madame Maxime, provided he could manage it.
After her initial shock, Pomona sank into anxiety again. She did not go to Hagrid "at once, immediately." After all, she had to "remind" him to mind his appearance without