We have performed a near-edge x-ray absorption fine-structure (NEXAFS) investigation of multi-walled boron nitride nanotubes (BNNTs). We show that the one-dimensionality of BNNTs is clearly evident in the B K edge spectrum, while the N K edge spectrum is similar to that of layered hexagonal BN (h-BN). We observe a sharp feature at the σ* onset of the B K edge, which we ascribe to a core exciton state. We also report a comparison with spectra taken after an ammonia plasma treatment, showing that the B K edge becomes indistinguishable from that of h-BN, due to the breaking of the tubular order and the formation of small h-BN clusters.