Just to clear something up. People have rights. Government Agencies and their employees have authority. Two very different things.
I've had the "pleasure" of explaining that to many agents of the government and in its own way puts them in their place with out being too rude/aggresive. Especially when reminding them that my rights can't be taken away by them but their authority in doing their job can be taken away if they violate my rights.
As for the privacy filter on the screen I imagine it's there for many reasons. To prevent disclosure to someone else who could see the screen while going through Immigration, prevent viewing of personal data by someone you're traveling with. My family has traveling with my brother's gf before they got married and we were processed as one group so a disclosure of one person's information could cause internal family problems. Yes you can get the information that indicated for secondary inspection via requests about your own self. Do so if you feel it's worth it.
CBP does post signage about not using your cell phones in the immigration hall. Not sure if it's law or policy. I believed you did the right thing by identifying that you're contacting your legal rep and proceeding with the call. Proceed with your fight if you want but be ready for more secondary searches.