I’m guessing they do not want you to go in and take photos of the screen because they cannot control the safety of PHI of other patients - like if you go in behind the counter and somebody else’s profile was pulled up on another screen that ends up in your photo, or you rush to the keyboard and start flipping through records before they can stop you. It is reasonable to expect to receive copies of your PHI in paper or electronic (email? flashdrive?) form, I wouldn’t demand more.

What is odd is that the papers they have given you are missing dates. I am guessing this is not malicious intent to deceive on their part, but rather some odd deficiency with their computer system which they are too embarrassed/unable to explain. When it prints it doesn’t come out the way it shows on the screen. Given how they have tried to fix the problem by writing in the dates manually, they are not trying to hide the dates per se. I would just let it go and accept the papers as is, unless you have specific reason to believe the dates are incorrect. You could even ask them to write a statement at the bottom to the effect of “dates are correct as shown, written by hand to circumvent a computer problem” with the office signature/stamp. Then even if it comes to legal proceedings or whatever, the court can treat handwritten documents the same as printed ones.