Myoelectric control, the use of electromyogram (EMG) signals generated during muscle contractions to control a system or device, is a promising modality for enabling always-available control of emerging ubiquitous computing applications. However, its widespread use has historically been limited by the need for user-specific machine learning models because of behavioural and physiological differences between users. Leveraging the publicly available 612-user EMG-EPN612 dataset, this work dispels this notion, showing that true zero-shot cross-user myoelectric control is achievable without user-specific training. By taking a discrete approach to classification (i.e., recognizing the entire dynamic gesture as a single event), a classification accuracy of 93.0% for six gestures was achieved on a set of 306 unseen users (who provided no training data), showing that big data approaches (compared to most EMG studies, which typically employ only 10-20 users) can enable robust cross-user myoelectric control. By organizing the results into a series of mini-studies, this work provides an in-depth analysis of discrete cross-user models to answer unknown questions and uncover new research directions. In particular, this work explores the number of participants required to build cross-user models, the impact of transfer learning for fine-tuning these models, and the effects of under-represented end-user demographics in the training data, among other issues. Additionally, in order to further evaluate the performance of the created cross-user models, a completely new data set was created (using the same recording device) that includes known covariate factors such as cross-day use and limb-position variability. The results show that the large data models can effectively generalize to new datasets and mitigate the impact of common confounding factors that have historically limited the adoption of EMG-based inputs.