Chondrules and matrices make up most of the bulk of chondrites. Chondrites have elemental compositions close to that of the Sun except for volatility related depletions and iron fractionation relative to silicon. Being igneous, chondrules are volatile depleted, while their host matrices are considered to have assembled mostly from low-temperature (volatile-rich) material. There is an outstanding controversy as to whether (i) chondrules and matrices formed independently and subsequent mixing of these components explains the departure of chondrite compositions from solar abundances for major elements, or whether (ii) their complementary patterns imply that the two dissimilar components were formed together from a reservoir with a solar composition and accreted without being separated to maintain this solar composition. The question around which this controversy centers has important implications for our understanding of the working of the protoplanetary disk, as complementarity between chondrules and matrices would rule out some chondrite formation models, such as those that imply an origin of these components from widely separated parts of the disk. In the present paper, we discuss literature data for chondrules, matrices, and bulk carbonaceous chondrites. We point out that, except for those of the CI group, all chondrites are fractionated with respect to the Sun for all major and minor elements across the condensation temperature range. We show that bulk chondrite compositions are better reproduced by adding a generic chondrule composition to the proper amount of CI-composition matrix, rather than by combining the in situ measured compositions of their chondrules and matrices. These results indicate that chondrule and matrix compositions in any given chondrite are not genetically related to one another. We also discuss the case of moderately volatile elements, for which a similarity of patterns between chondrules and matrices has been reported, and argue that this similarity was established as a result of exchange during alteration on the chondrite parent body and does not reflect a common nebular reservoir. Last, we contend that the recently discovered tungsten and molybdenum isotopic differences between chondrules and matrices argue in favor of distinct isotopic reservoirs for these chondritic components and hence against a genetic relationship between chondrules and their host matrices. A time interval between the formation of chondrules and of matrices and long-range relative transport of these components in the disk are, therefore, not ruled out by existing chemical and isotopic constraints.