Generally the flat side of the washer goes to the pan and the rounded edge side to the bolt. The reason they claim is that when these things are cut out by the press the bottom is pressed flatter while the top is slightly rounded.
The flatter side of the washer goes to the flatter or machined surface which would be the pan, brake caliper or other housing while the slightly rounded part gets crushed by the bolt. The bolt edges are flats and don't require sealing in that area.
Personally I don't think it makes a lick of difference, if it did they would use a ground on both sides washer like they do inside some transmission, diffs, etc.