We have to control our borders and control immigration. But that doesn't mean we throw the Fourth and Fourteenth Amendments into the garbage bin at the same time. The Arizona law which permits police officers to, having stopped anyone because of some infraction, require the person to show proof of citizenship is heaving those amendments into the wastebasket.
The only people who are going to be asked for their "papers" are those who "look" like they may be in the country illegally. What constitutes such a "look"? Good question. Since I'm caucasian I could rob a bank in Arizona and, after being caught, it's very very unlikely I would be asked for my citizenship papers (I don't know what I would show anyway...my birth certificate? I don't carry that with me). Someone with that "look" could be stopped for a broken taillight and find him/herself being under suspicion based on looks alone. So, it doesn't matter if the person is a citizen, in fact could be a multigenerational citizen of the U.S., that person is presumed guilty until proven innocent.
That's the point of this drawing. The officer is demanding the "papers" of a petroglyph which has been in this region for the past 1000 years, before there was a U.S. to be a citizen of.