Ancient, SiO2-rich achondrites have previously been proposed to have formed by disequilibrium partial melting of chondrites. Here, we test the alternative hypothesis that these achondrites formed by fractional crystallization of impact melts of Rumuruti (R) chondrites. We identified two new melt clasts in R chondrites, one in Pecora Escarpment (PCA) 91241 and one in LaPaz Icefield (LAP) 031275. We analyzed major, minor, and trace element concentrations, as well as oxygen isotopes, of these two clasts and a third one that had been previously recognized (Bischoff et al. 2011) as an impact melt in Dar al Gani (DaG) 013. The melt clast in PCA 91241 is an R chondrite impact melt closely resembling the one previously recognized in DaG 013. The melt clast in LAP 031275 has an L chondrite provenance. We show that SiO2-rich melts could form from the mesostases of R chondrite impact melts. However, their CI-normalized rare earth element patterns are flat, whereas those of ancient SiO2-rich achondrites (Day et al. 2012; Srinivasan et al. 2018) and those of disequilibrium partial melts of chondrites (Feldstein et al. 2001) have positive Eu anomalies from preferential melting of plagioclase. Thus, we conclude that ancient SiO2-rich achondrites were probably formed by disequilibrium partial melting (due to an internal heat source on their parent bodies), rather than from impact melts.