Mostly when you meet in person, even if they know the answer will be no, they will demur. The don't like face-to-face nos.
But later they will send a letter or make a phone call and say they can't support you in what you want.
They may give a reason such as, "leadership is against this and I can't oppose them."
You can explore their reasoning by asking this question in these exact words:
"You must have some reason for feeling that way, can you tell me what it is?"
Then, and this is important, resolve to find something you can get a "yes" on; you don't want to leave on a "no."
It may be as simple as "I understand you can't help us now, can we send you some more information in hopes of changing your mind?"
Always leave on a positive note.