Since the principles of photography post-dated the Constitution, I'd say it's a fair assumption that in its time the expectation was that exclusive access would be needed to (laboriously) copy something.

But it's kind of pedantic to argue over a single word.

The pertinent question is 'Do the views espoused by the Constitution as a whole (and subsequent case law) offer an opinion on the rightness of mass copying-without-exclusive access?'

Which is pretty thorny indeed. IANAL, but from what I've read it seems as though the Supreme Court is steadily trending more towards supporting an inherent right to privacy as a buttress against decisions that would otherwise feel wrong.

This is actually a great point. For all those folks who say violating copyright is not "stealing", I guess you could use the same argument that the gov't copying private records is not "seizing".