(1) Bank statements are so easy to Photoshop up. If you're smart, you're always a "cash buyer" even if you're looking to get a mortgage, if you know what I mean. Asking for paperwork just to view the house will just make a lot of people not want to go through the trouble without actually weeding out the "speculators." Save the paperwork for the binding offer stage.
(2) The "looky loos" aren't always a bad thing. People talk, and they might tell someone else about the house.
(3) I'm surprised that they're whinging about it being built in 1989, considering a lot of the housing stock in the DC region is a lot older. Were those maybe people who recently moved from the West Coast or Phoenix, where 1980s can often be old.
(4) Never be insulted by negotiation tactics. It's a game. Play or be the water boy.