The last three times I have stayed in hotels in the states, my drivers license was scanned and returned to me. No photocopying necessary.
When I lived in Europe, and stayed in hotels, the front desk kept my passport overnight, as the police came in and checked on who was staying in the town's lodging facilities.
There may be something to the Homeland Security thing, but I don't know of any requirement by DHS to keep records of transients.
I would think the hotels or campgrounds may keep the record not so much for homeland security purposes, but for assessment of any additional charges for damages once you check out.
