Recent media stories have reported that online webcam-based exam proctoring have wrongly flagged students for cheating, causing tremendous anxiety and frustration, and thus disadvantaging students. This study assesses if online webcam-based exam proctoring in the age of COVID-19 disadvantages students (particularly those who are non-white and with different ethnic and socio-economic status), and whether worry about being wrongly flagged for cheating may affect students' exam performance. This survey-based study was conducted using 237 undergraduate students enrolled in a public land-grant research university in the upper Midwest region of the United States, who took their exams through Proctorio. Our study supports -- as is widely reported by the media -- that students are experiencing anxiety and fear of being wrongly flagged during online proctoring. However, we show that students' anxiety about online proctoring is associated with their general level of anxiety; this correlation to "trait" anxiety supports our previous study. We further find that worry over being wrongly flagged did not directly impede students' exam performance. We discuss how students and faculty alike face challenges, especially those who had not used online webcam exam proctoring prior to COVID-19 stay-at-home directives. For faculty, it is not only having to adapt to an unfamiliar teaching environment that requires new technologies, but also being expected to utilize webcam-based online proctoring for high stakes exams. An in-depth look is needed into the kind of support students and faculty need using online proctoring into the future. Furthermore, the academic world in general, and US colleges and universities in particular, should initiate a conversation on how best to regulate this industry so that students and institutions are well served.