Given the growing use of generative artificial intelligence as a tool for creating multilingual content and bypassing traditional translation methods, this study explores the ability of linguistically trained individuals to discern machine-generated output from human-written text (HT). After brief training sessions on the textual anomalies characteristic of synthetic text (ST), twenty-three postgraduate translation students analysed excerpts of Italian prose and assigned likelihood scores to indicate whether they believed they were human-written or AI-generated. The results show that, on average, the students struggled to distinguish between HT and ST, with only two participants achieving notable accuracy. Closer analysis revealed that the students often identified textual anomalies in both HT and ST, although features such as low burstiness and self-contradiction were more frequently associated with ST. These findings suggest the need for improvements in the preparatory training. Moreover, the study raises questions about the necessity of editing synthetic text to make it sound more human-like and recommends further research to determine whether AI-generated text is already sufficiently natural-sounding not to require further refinement.