The Source of the School District's Mistaken Belief

The school district also mistakenly believed that Kastoroff's numbers added up to just under $90,000.

They did not arrive at this belief by adding up the numbers themselves. They formed the belief when they opened Kastoroff's bid (on the ground that no reasonable contractor would bid less than it cost to do the job).

The school district just takes the contractor's word for it, they do not make an independent judgment about whether the bid accurately reflects the costs of the work.

The school district makes an independent judgment about whether the bid accurately reflects the costs of the work.