McCreed is correct and I am not. My apologies but I have led you astray by not checking the logic of the DiMarzio diagram. I just assumed that since it was indexed under "2 humbucker, 3-way switch, 1 volume, 1 tone, neck, neck/bridge, bridge" that it would be the correct diagram. I think the DiMarzio diagram is incorrect, and that you wired it up perfectly. Here is my analysis diagram. Green dots indicate the lugs that are connected on that side of the switch for each position, red dots indicate the lugs that are connected on the other bank. The top row of diagrams shows the result for each blade position using the DiMarzio wiring. The bottom row corrects the mistakes.
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However, you can see that all that is required is one extra link on each side for the middle switch position to select both pickups. So if your friend ever returns the guitar it will be easy to fix.

Plus you should be pleased that you followed the diagram perfectly, it's the DiMarzio switch wiring that is wrong. My apologies once again for that.