Gah. Dreamed about leaking pipes and problems lurking inside the walls of my house all night.

I am going to be positive, though. Positive that they CAN fix it. (That pipe, on second look, might in fact be iron and not lead, a resource I checked said lead was mostly used pre 1920s and I think my house was built in the late 40s.) I think I know what happened to the pipe: two different metals (the old pipe and the newer pipe that makes up the trap). The thing acted like a battery and a reduction-oxidation reaction took place and corroded the old pipe (The old pipe was the anode).