Buzz behind the saddle? Are you sure it isn't the saddle itself? Check how it is seated in, that the bottom of the saddle is smooth and flat, and that the seating area is also nice and smooth and flat. Equally you could look at the seating of the ball string ends. To get buzz (other than fret buzz) you need something that is either:
not seated correctly, so it moves, even under tension
where the string is routed through or next to something with insufficient space so that string vibration touches the close surface
Granted, depending on how the ball ends are secured it is possible that the string could touch another surface, I would think it unlikely as the length of string between the ball end and the saddle is very short so string movement will be limited.
Is it an electro acoustic? Most electro acoustics have the bug under the saddle. If that is not seated correctly it could provide a pivot point allowing saddle movement.
I must have written my post at the same time as Hobo, and it looks like we are thinking in a very similar way.