When I export Illustrator artwork as a png file, I get a one pixel grey border at the top and left edges.
There is no background object, but I export (Save for Web and Devices) with matte white background and no transparency. I also tried with a white background object, with it snapped to the artboard and also larger than the artboard by 10 pixels in each direction. I still got the lines at the top and left of the exported image.
I also tried making a new file, with the artboard in pixel units, and selected the option to have objects snap to pixel grid, and then copying and pasting the artwork from the original file. I still got the lines.