In the United States, the opioid overdose crisis disproportionately affects incarcerated individuals, with opioid overdose risk in the two weeks after release 50 times higher than the general population. As a response, many prisons and jails are starting to offer medication for opioid use disorder (MOUD), including methadone or buprenorphine, during incarceration or prior to release. One implementation barrier is how to identify who would benefit from treatment, given that opioid use disorder screening and diagnostic testing are imperfect, particularly in criminal-legal settings. Prisons and jails use a variety of OUD assessment strategies, including brief self-report screening tools, diagnostic interviews, review of pre-incarceration medical records, and urine drug screening, all of which may lead to false positive and false negative results. In this essay, we apply a common framework from epidemiology and other fields to conceptualize OUD assessment in carceral settings: individuals assessed for OUD can be those with OUD who are correctly offered MOUD ("true positives"), those without OUD who are offered MOUD ("false positives"), those with OUD who are not offered MOUD ("false negatives"), and those without MOUD who are not offered MOUD ("true negatives"). We discuss these assessment and treatment outcomes from the perspectives of people who are incarcerated, security staff, and healthcare staff. This framework may inform discussions between medical staff and security personnel on the implementation of MOUD programs.