Montiaceae comprise a clade of at least 270 species plus about 20 accepted subspecific taxa, primarily of western America and Australia. The present paper is the first of a two-part work that seeks to evaluate evolutionary theory via metadata analysis of Montiaceae. In particular, it uses metadata analysis to evaluate the theory in theory-laden methods that have been applied in evolutionary analyses of Montiaceae. This part focuses on phylogeny and phylogeography. The second part focuses on phenotypic and ecological diversification. An emergent theme in this paper is the degree to which historical idiosyncrasy during Montiaceae evolution misleads quantitative methods of evolutionary reconstruction and phylogeographic interpretation. This suggests that idiosyncraticity itself is a fundamental property of evolution. The second part of this work elaborates this notion as the Principle of Evolutionary Idiosyncraticity. The present part describes idiosyncraticity in molecular phylogenetic and phylogeographic data and uses this notion to refine ideas on Montiaceae evolution. Phylogenetic metadata conflicts and conflicting phylogeographic interpretations are discussed. I conclude that, owing to PEI, quantitative methods of evolutionary analysis cannot be globally accurate, though they are useful heuristically. In contrast, classical narrative analysis is robust in the face of PEI.