The possibilities and challenges of digital technologies for young children are widely documented. However, parental guidelines place greater emphasis upon potential harms, advocating that parents limit their children's screen time, or advise that parents simply read digital texts as they would a printed text. Our study investigated 22 Australian parents' perspectives of their 2-3-year-old child's experiences with digital devices and their views of reading digital storybooks to understand whether parents were cognisant of or engaged in practices that appeared to limit their child's screen time, and whether parents noted any differences when shared reading printed and digital texts with their child. Results showed that many parents (1) limit screen time and therefore do not engage in shared digital text reading, consigning children's screen time to unsupervised use; and (2) were aware that the reading of digital texts often is, and at times should differ to the reading of printed texts. These findings suggest that advising parents to limit screen time may result in parents avoiding the use of digital texts when shared reading with their child. Furthermore, recommending that parents read digital texts as they would printed texts may encourage parents to have unrealistic and/or frustrating expectations.