Recent models attempting to explain non-mass-dependent oxygen isotopic anomalies in meteorites and planets posit that they may have originated within the gas phase of the solar nebula, which suggests the potential for correlations of non-mass-dependent oxygen isotopic anomalies with other chemical fractionations generated during cooling and condensation of the nebula. We have examined three specific issues: possible correlations of Δ17O with (i) oxidation state; (ii) bulk chondrite chemistry; and (iii) bulk planetary properties. Isolated grains and chondrules from several carbonaceous chondrite groups exhibit good to weak positive correlations between Δ17O and olivine fayalite content, and whole rock ureilite samples show a positive correlation of Δ17O with olivine fayalite content. These are consistent with oxidation of Fe metal by 17O-, 18O-enriched oxygen in the precursor materials that formed these objects. In contrast, oxygen isotopic and major element compositions of ferromagnesian phases in ordinary chondrite chondrules, and in bulk chondrites do not show a correlation. Thus, there is no compelling evidence that oxidation of nebular materials was tightly linked to gas species carrying anomalous O. Using average chondrite group compositions, we demonstrate that significant negative correlations of refractory lithophile element/Mg and refractory siderophile element/Ni with Δ17O exist. Refractory inclusions (CAIs and AOAs) are modally rare in many chondrite types that exhibit substantial range in Δ17O. Thus, the refractory component in these chondrites must occur in a crypto-component, e.g. material dissolved in chondrule melts during chondrule formation. Significant positive correlations of moderately volatile elements/Mg with Δ17O are not simply explained by incomplete mixing of 16O-enriched refractory grains, but are broadly consistent with nebula-based mechanisms of non-mass-dependent oxygen isotope fractionation. The estimated compositions of the primitive mantles of the Earth, Mars and 4 Vesta have some compositional, redox and isotopic properties that vary with heliocentric distance. However, Δ17O does not vary monotonically in this sequence, indicating a decoupling of planetary O isotopic composition from other compositional characteristics.