As an outside example: in "Call of Cthulhu," investigators delay calling in the mortal authorities until absolutely necessary, for a few good reasons. 1) The mortal authorities are usually woefully unequipped to deal with a given supernatural threat, and 2) this lack of understanding may mean that the investigators get locked up, unable to oppose the evil force they were facing.
While reason 1 usually doesn't apply to the Wardens, reason 2 is still a fine motivator. DFRPG protagonists are routinely set up to look suspicious, and well-intending but thorough Wardens can easily tie up a player group while precious time trickles by. Most groups are probably motivated to avoid the Wardens simply out of a sense of self-preservation: it is easier to face a tribunal when the mystery has been solved.