I always screenshot mine so I know I can access it regardless of connectivity. Problem is, a screenshot proves nothing as it is very easily shared and even modified, so it could be anyone's pass. No venue has the resource to check the source of each individual pass on entry, so it is all entirely done on trust, which in turn makes the checks themselves redundant since those that can be trusted to present a genuine Covid pass can probably be equally trusted to do what they are obliged to do regardless of whether or not someone is checking.