Anytime we have had clients in this situation, the insurance company usually put the rebuild to tendor and then go for the lowest bid from a reputible builder. They usually have the right to do this in their t&c's. I would think in the current environment they may be even more inclined to do this. I have heard that a lot of independent assessors working on behalf of the client have been able to optain a chq from the company (I would think this is to facilitate them getting paid, thats not to say the assessor is not worth paying for, they usually are in a big claim), but don't think this is a certainty.