Flying schools and other commercial operators require their Operations Manual to specify procedures for use of EFBs so must comply with the rules in the CAO and, of course, whatever their local CASA FOI requires ... which most likely will be that recommendation.Who is affected by the EFB regulations?
So, when the flight school tells you something I can only assume that the context is while you are training so what they state must be in accordance with their Operations Manual? If not, they are probably giving you good advice but they are not telling you what the law is. In private operations you get to make the decision yourself.
If I'm going somewhere busy and/or somewhere I'm not familiar with then I want everything going for me. If I'm going on a dawdle which CASA would say is a cross-country then I might go with just the iPhone and I would get through a ramp check per Ramp checks | CASA Out-n-Back
Read the CAAP Electronic flight bag
"This CAAP looks to provide guidance for the use of EFB by Air Operator’s Certificate (AOC) holders as they are bound to meet the obligations detailed in the AOC conditions set out in Appendix 9 of CAO 82.0. ....... The CAAP will also provide general guidance for private operators." There are nil requirements for private operators regarding this discussion.