A high proportion of non-users of news is considered a concern for a functioning democracy. However, existing empirical assessments on the share of news avoiders rely exclusively on survey data and the results vary drastically between studies, making it difficult to evaluate the severity of the issue. This study relies on tracking data of Swiss Internet users and applies and discusses two computational methods, identifying news at the domain and article level, to realistically assess the extent of non-users of online news. Results indicate that at least 14.2% of Internet users do not use news online. Furthermore, this study suggests that identifying news use solely based on tracking data at the domain level is distorted by a faux news effect, i.e., non-news use on news domains, and an invisible news effect, i.e., news use on small and unknown news domains. The parallel use of tracking data and supervised text classification allows to dissect and discuss these effects systematically. Similarly, it is found that not accounting for news use via apps overestimates the extent of non-use of online news. The findings provide valuable insights for future applications of these methods in similar contexts.