The whole paper just discusses “hypotheses” meaning they are just guesses without evidence. The first summary paragraph says: “Several hypotheses have been proposed to explain these observations, including independent invention of DNA and DNA replication proteins, ancient gene transfer and gene loss, and/or nonorthologous replacement.”

Citation: https://www.ncbi.nlm.nih.gov/books/NBK6360/

Summary

The transition from the RNA to the DNA world was a major event in the history of life. The invention of DNA required the appearance of enzymatic activities for both synthesis of DNA precursors, retro-transcription of RNA templates and replication of singleand double-stranded DNA molecules. Recent data from comparative genomics, structural biology and traditional biochemistry have revealed that several of these enzymatic activities have been invented independently more than once, indicating that the transition from RNA to DNA genomes was more complex than previously thought. The distribution of the different protein families corresponding to these activities in the three domains of life (Archaea, Eukarya, and Bacteria) is puzzling. In many cases, Archaea and Eukarya contain the same version of these proteins, whereas Bacteria contain another version. However, in other cases, such as thymidylate synthases or type II DNA topoisomerases, the phylogenetic distributions of these proteins do not follow this simple pattern. Several hypotheses have been proposed to explain these observations, including independent invention of DNA and DNA replication proteins, ancient gene transfer and gene loss, and/or nonorthologous replacement. We review all of them here, with more emphasis on recent proposals suggesting that viruses have played a major role in the origin and evolution of the DNA replication proteins and possibly of DNA itself.