and have absolutely no control over who can or cannot walk on them or what a person does while they are walking on them. They have no right to know who you are or what you are doing and you don't owe them any "respect" for anything. If they want privacy for their patrons they can draw the shades.
"It is a cordial conversation but your are trying run this conversation and that's not how this is going to go?"
That's "respectful" to you? Who does this LEO think they are talking to a law-abiding member of the public in this manner? They are not you mommy or daddy. Talk about "privilege". Taking pictures and/or video in a public place or of subjects that can be viewed from public spaces cannot be used as a pretense, in the guise of "suspicious activity", to initiate an investigation. Absent the suspicion of an actual crime being committed, you are under no obligation to say anything to them let alone provide ID. That's not being evasive that's exorcising your rights. We don't have "papers please" in the US. Finally, do you see the ridiculousness of walking up to someone who is obviously taking pictures and video and telling them you don't want to have a picture or video of you taken?
"And although the citizen was within his rights" is all that's required here. ...end of discussion. Know your rights. Use your rights.