Despite everything Vaan said, they were all assumptions. Thus, a single piece of incorrect information would make it all wrong.
Nevertheless, Transcendent Sybil must have done some research on Baron Chalfont to believe Dorothy was precious to him.
Perhaps Dorothy lived with her mother in the Kingdom of Verdant Woods because Baron Chalfont purposely sent them there. The environment was certainly more suitable for witches than the Holy Knight Empire.
That said, Baron Chalfont's importance wasn't Vaan's biggest concern; it was the Holy Knight Empire's desire.
If the Holy Knight Empire itself wanted war with the Kingdom of Black Rose to happen, Baron Chalfont's role would become inconsequential.
They just needed justification for starting the war.
Alas, there wasn't enough information on the Holy Knight Empire. Thus, it was impossible for Vaan to anticipate their move accurately.
Everything came down to information.