See
this page in the manual about home contact
As it says "this form can be returned electronically" on the forms, and IF you can guarantee access to the information then no, you don't need to print it out. Personally, I would advise common sense, if you're taking the girls to an event for an hour on a Saturday, your phone/tablet is unlikely to die in that time, provided you've downloaded the forms before going, just in case you don't have internet, then the risk of being without the information you need is negligable.
However, if you're off on a full day trip, which involves (as examples, not to be taken as gospel) coaches and/or adventurous activities, basically where the girls are going to be in your care for much longer etc, I would definitely advocate hard copies, just in case your technology fails. Whether you ask parents to print and return, or whether you print them, out, that's up to you.
I know the manual is not the most user-friendly if you're looking for something specific, but I think you would find it very useful to spend an evening taking a look through it.