the sod is dead. if you just had it installed, there is no way that it should look that bad. one purpose of sod is for instant impact. even when sod is dormant, it won't be completely brown.
from the picture, the prep work also looks pretty bad. was the soil level, and free of rocks and debris? roots will not grow into the soil, if there is not good contact between the base of the sod and the top of the ground.
Don't pay for anything. As others said, the sod was dead when they installed it. Once cut at the farm, you need to lay it in a day or two max. Leaving it rolled up on a pallet, its going to dry out pretty quickly. Also, if you had temps in the 80's or 90's and it was left in the sun, the sod would toast alot more quickly. As for watering, the sod needs to stay moist as well as your existing ground. You don't want puddles or standing water under the sod, but it needs to stay damp until rooted.
Did you have a contract for the work, and is there anything in there to get rid of the contractor or void the contract. The contractors work really does not seem on the up and up, and I would be very concerned if he actually believed this sod would come back.
I would get a new, reputable contractor to redo the whole project.