Bulk chondritic meteorites and terrestrial planets show a monotonic depletion in moderately volatile and volatile elements relative to the Sun's photosphere and CI carbonaceous chondrites. Although volatile depletion was the most fundamental chemical process affecting the inner solar nebula, debate continues as to its cause. Carbonaceous chondrites are the most primitive rocks available to us, and fine-grained, volatile-rich matrix is the most primitive component in these rocks. Several volatile depletion models posit a pristine matrix, with uniform CI-like chemistry across the different chondrite groups. To understand the nature of volatile fractionation, we studied minor and trace element abundances in fine-grained matrices of a variety of carbonaceous chondrites. We find that matrix trace element abundances are characteristic for a given chondrite group; they are depleted relative to CI chondrites, but are enriched relative to bulk compositions of their parent meteorites, particularly in volatile siderophile and chalcophile elements. This enrichment produces a highly nonmonotonic trace element pattern that requires a complementary depletion in chondrule compositions to achieve a monotonic bulk. We infer that carbonaceous chondrite matrices are not pristine: they formed from a material reservoir that was already depleted in volatile and moderately volatile elements. Additional thermal processing occurred during chondrule formation, with exchange of volatile siderophile and chalcophile elements between chondrules and matrix. This chemical complementarity shows that these chondritic components formed in the same nebula region.