This paper provides a critical analysis of the molecular mechanisms presently used to explain transcriptional strand asymmetries of single base substitution (SBS) signatures observed in cancer genomes curated at the Catalogue of Somatic Mutations in Cancer (COSMIC) database (Wellcome Trust Sanger Institute). The analysis is based on a deaminase-driven reverse transcriptase (DRT) mutagenesis model of cancer oncogenesis involving both the cytosine (AID/APOBEC) and adenosine (ADAR) mutagenic deaminases. In this analysis we apply what is known, or can reasonably be inferred, of the immunoglobulin somatic hypermutation (Ig SHM) mechanism to the analysis of the transcriptional stand asymmetries of the COSMIC SBS signatures that are observed in cancer genomes. The underlying assumption is that somatic mutations arising in cancer genomes are driven by dysregulated off-target Ig SHM-like mutagenic processes at non-Ig loci. It is reasoned that most SBS signatures whether of "unknown etiology" or assigned-molecular causation, can be readily understood in terms of the DRT-paradigm. These include the major age-related "clock-like" SBS5 signature observed in all cancer genomes sequenced and many other common subset signatures including SBS1, SBS3, SBS2/13, SBS6, SBS12, SBS16, SBS17a/17b, SBS19, SBS21, as well as signatures clearly arising from exogenous causation. We conclude that the DRT-model provides a plausible molecular framework that augments our current understanding of immunogenetic mechanisms driving oncogenesis. It accommodates both what is known about AID/APOBEC and ADAR somatic mutation strand asymmetries and provides a fully integrated understanding into the molecular origins of common COSMIC SBS signatures. The DRT-paradigm thus provides scientists and clinicians with additional molecular insights into the causal links between deaminase-associated genomic signatures and oncogenic processes.