Gene tree discordance in large genomic datasets can be caused by evolutionary processes such as incomplete lineage sorting and hybridization, as well as model violation, and errors in data processing, orthology inference, and gene tree estimation. Species tree methods that identify and accommodate all sources of conflict are not available, but a combination of multiple approaches can help tease apart alternative sources of conflict. Here, using a phylotranscriptomic analysis in combination with reference genomes, we test a hypothesis of ancient hybridization within the plant family Amaranthaceae s.l. that was previously supported by morphological, ecological, and Sanger-based molecular data. The dataset included seven genomes and 88 transcriptomes, 17 generated for this study. We examined gene-tree discordance using coalescent-based species trees and network inference, gene tree discordance analyses, site pattern tests of introgression, topology tests, synteny analyses, and simulations. We found that a combination of processes might have generated the high levels of gene tree discordance in the backbone of Amaranthaceae s.l. Furthermore, uninformative genes and model misspecification also contributed to discordance. Overall, our results suggest that Amaranthaceae s.l. might be a product of an ancient and rapid lineage diversification, and remains, and probably will remain, unresolved. This work highlights the potential problems of identifiability associated with the sources of gene tree discordance including, in particular, phylogenetic network methods. Our results also demonstrate the importance of thoroughly testing for multiple sources of conflict in phylogenomic analyses, especially in the context of ancient, rapid radiations. We provide several recommendations for exploring conflicting signals in such situations.