Your question seems based on sheet-fed technology, when (correct me if I'm wrong), these would have been printed by rotary presses on roll-stock, then fed from the roll through the perforator, then cut into panes. I see no way a roll could have been fed twice in any manner. I don't know the answer, but would seek an explanation which takes into account the printed web being a full press sheet wide (and thus symmetric), and the machine direction of travel (which perfs were added in the machine-direction and which in the cross-direction?).
This may be from Giori Press and fed into sheet-fed L-Perforator which consisted of two rotary wheel perforators linked at right angles to each other by a conveyor belt system. Thus, if it was fed twice into the perforator, the double line perforation error would occur in both directions rather than just one.
The following essay was originally presented in the Millenium Edition of the Linn's World Stamp Almanac, 6th Edition (2000) - Hotchner
"When a sheet in error went through half the process, it should have probably been pulled or destroyed. Instead some were probably bunched with imperforates and sent through the entire process again. Since one edge of the sheet had already been trimmed on the first pass, the sheet was out of registration by the amount trimmed when it went through a second time. Thus the doubled set of perfs is shifted an equal distance to the amount originally trimmed. "
So jogil, perhaps the sheet had no perforations running horizontally, and readded to the batch, and got the horizontal perforations, but then resulted in a doubling vertically. Sounds reasonable-ish. Might have to form a collect of these :)