Chris' answer of "smoke-laden moisture" is spot on, no surprise, and anyone and everyone ought to check out all the info he has here on his site.
Only thing I'd add though is that rusty residue can happen without water in the pan as well, if you cook a lot of meat at once. I often load up my cooker with poultry using a dry pan and get the rusty residue just as if I was doing a low-n-slow with water. Of course, it depends on how moist your birds are, so if you air dried them, probably not. I usually get plenty of rusty looking residue from cooking two racks of chicken just pulled out of a marinade or buttermilk brine, though. I just check my domes between cooks and hit the high spots and rinse out as needed. I'd rather be outside and do that than wash pots and pans, any day.