There are a variety of reasons for folks to want to know your salary
history, sadly none of the reasons are in your best interest.  However,
you are kind of between a rock and a hard place.  You have to give them
some sort of answer unless you really have a lock on the job.  I suggest
being vague high 30's that sort of thing, play up how important fringes
were.
But back to why
1. Sometimes a board really has very little idea of what a job should pay
and are looking for info.
2. A board may be looking forward to neg. and wants to have the upper
hand.  If you have been working for say 50K  it is hard to argue for more
than a 25% raise, even if your predecessor was making 80K. Exactly what
happened at one mid sized museum.  The new director had to sign the last
couple of checks for old one-boy was he unhappy
3. It is a way of screening out people  who have unrealistic
ideas of what the institution can pay.
4. To some extent it helps define what someone's role really was. A
collection manager, for example, can range from little more than a clerk
to a highly trained experienced professional.  Pay gives a hint.
3.