Ehh, if the mechanism isn't completely understood I guess we aren't expected to understand it; but tubulointerstitial injury makes sense I guess-- is it possible for the hypercalcemia to cause calcium deposits to solidify in the DCT, resulting in some sort of physical injury to the receptors in the DCT?
Clinically there's a distinction between partial and complete nephrogenic DI (and one extremely annoying UWorld question I still remember 2 years later). Hypercalcemic crisis causes partial nephrogenic DI, so you still maintain some capacity to concentrate urine. The mechanism isn't that controversial. Down-regulation of aquaporin-2 channels in the medulla.