The opioid crisis has disproportionately affected U.S. veterans, leading the Veterans Health Administration to implement opioid prescribing guidelines. Veterans who receive care from both VA and non-VA providers-known as dual-system users-have an increased risk of Opioid Use Disorder (OUD). The interaction between dual-system use and demographic and clinical factors, however, has not been previously explored. We conducted a retrospective study of 856,299 patient instances from the Washington DC and Baltimore VA Medical Centers (2012-2019), using a deep neural network (DNN) and explainable Artificial Intelligence to examine the impact of dual-system use on OUD and how demographic and clinical factors interact with it. Of the cohort, 146,688(17%) had OUD, determined through Natural Language Processing of clinical notes and ICD-9/10 diagnoses. The DNN model, with a 78% area under the curve, confirmed that dual-system use is a risk factor for OUD, along with prior opioid use or other substance use. Interestingly, a history of other drug use interacted negatively with dual-system use regarding OUD risk. In contrast, older age was associated with a lower risk of OUD but interacted positively with dual-system use. These findings suggest that within the dual-system users, patients with certain risk profiles warrant special attention.