I'll set aside my usual rant about making educational decisions based on a single test score. It's illegal to make educational decisions that way for disabled students, why do schools keep doing it for gifted programs?
Letting it go, letting it go...
Cognitive scores are notoriously unstable for kids under about 8 years old. That explains the school's reluctance to put much stock in it. It also may explain the discrepancy. The reality is that the different instruments measure different things. The KBIT would be a test you would give a much younger student, that does not weight verbal scores as heavily as one aimed for an older student. If the only cognitive score a school had was a KBIT, they would want to retest when the student was a little bit older. After that, they would probably use the same cognitive scores until the end of time.
Personally, I had an IQ in second grade that was about 24 points lower than the one that I had in sixth grade. A 24 point discrepancy between two tests for an older student would be outrageous, but a 24 point discrepancy for a seven year old is about par for the course.
