Before their conversation that day, Dumbledore had been thinking about how to persuade Vaughn to meet the Chinese delegation, then-
"Sound them out" about what they wanted.
But now, he was beginning to regret it-
Dumbledore felt that arranging a meeting between Vaughn and the Chinese might turn out to be a terrible decision.
Naturally, that thought arose because the ideas Vaughn expressed and the direction of his actions were drifting further and further from what Dumbledore wanted to see.
Yet he had no choice.
In fact, one reason Dumbledore had been so enthusiastic about inviting China to the Potions exchange, spending months personally handling the arrangements, was, of course, his "deal" with Vaughn.
Vaughn would provide leads on Horcruxes, and he would help Vaughn solve his problems.
But he was also preparing for the future.
The changes in North America deeply unsettled Dumbledore. He had no idea what had happened over there, how Wilkinson-or rather, the DeSantises-had escaped death, what they were plotting, or whether their future influence would be good or bad.
That uncertainty was agonizing.
With an old wizard's political instincts, Dumbledore had no wish to wait passively for change to arrive. Bringing more international forces together was therefore the most effective strategy in the current, peaceful situation.
As one of the world's foremost magical powers, China was naturally the ideal "friend."
Essentially, he was using Vaughn's "platform" to pursue his own agenda.
So, even for the sake of his own plans, he had to accommodate the Chinese delegation's request to meet Vaughn.
But that did not mean he would simply give in at every turn. Over more than a century, Dumbledore had compromised many times, but never by surrendering.
This old dog still had a few teeth!
So the next day, he gathered the Hogwarts professors