In light of growing evidence that many parents are deeply concerned about their young children's increasing technology use, in this paper we report on aspects of a study funded by the UK Economic and Social Research Council, where we sought to understand parents' views on children's digital book reading. We introduced seven families to four award-winning digital books (story apps and e-books), observed how the mothers mediated their children's digital book reading over a period of several weeks and subsequently interviewed the mothers about their shared reading experiences with the digital books. Focusing on the interview data and drawing on the theoretical framework of socio-materiality, this paper reports on how parents' views about digital book features were entangled with their social perceptions of the value of digital reading. Analysis of parents' accounts show three conflicted themes of trust/mistrust, agency/dependency and nostalgia/realism in parental attitudes towards their children's reading on screens. The paper concludes with a discussion of how these findings regarding the unresolved dichotomies inherent in parental views about their children's digital reading are highly relevant for future research on parental mediation of their children's learning with digital media.