The question ultimately becomes should a diligent person, who has not heard of a testing institute before, investigate to determine if the testing institute is qualified to perform the evaluation. The secondary question, posed by Mark K, is if the building inspector has the authority to review the report issued by the engineer.
Here, the courts have been relatively clear that where a building officials encounters unfamiliar entities, it would be expected that they evaluate the capabilities and accreditations of those entities. This makes logical sense, as we can only be expected to rely on test reports from credible sources. On the question of reviewing an engineer's report, we already know we can do this. We do this everyday when reviewing plans and specifications that are stamped by engineers. In speaking with our local engineering society on the issue of questioning an engineer on their design, they indicated that we should always do this. If the engineer is unable to defend their report, it is not firmly rooted in acceptable engineering practice.
So to answer the question "what gives the building official the right to reject a report"
1. if the testing has been completed by an unaccredited testing laboratory
2. if the testing is outside of the testing laboratory's accreditation
3. if the report makes assumptions that do not align with the testing requirements
I have seen all of these. I have rejected their reports.