The so far unique role of our Solar System in the universe regarding its capacity for life raises fundamental questions about its formation history relative to exoplanetary systems. Central in this research is the accretion of asteroids and planets from a gas-rich circumstellar disk and the final distribution of their mass around the Sun. The key building blocks of the planets may be represented by chondrules, the main constituents of chondritic meteorites, which in turn are primitive fragments of planetary bodies. Chondrule formation mechanisms, as well as their subsequent storage and transport in the disk, are still poorly understood, and their origin and evolution can be probed through their link (i.e., complementary or noncomplementary) to fine-grained dust (matrix) that accreted together with chondrules. Here, we investigate the apparent chondrule–matrix complementarity by analyzing major, minor, and trace element compositions of chondrules and matrix in altered and relatively unaltered CV, CM, and CR (Vigarano-type, Mighei-type, and Renazzo-type) chondrites. We show that matrices of the most unaltered CM and CV chondrites are overall CI-like (Ivuna-type) (similar to solar composition) and do not reflect any volatile enrichment or elemental patterns complementary to chondrules, the exception being their Fe/Mg ratios. We propose to unify these contradictory data by invoking a chondrule formation model in which CI-like dust accreted to so-called armored chondrules, which are ubiquitous in many chondrites. Metal rims expelled during chondrule formation, but still attached to their host chondrule, interacted with the accreted matrix, thereby enriching the matrix in siderophile elements and generating an apparent complementarity.