One day after your post I received an email from Arduino support with the same information.
And yesterday I got two other Motor shield boards: One that I ordered directly from the Arduino.cc store, and another one from distributor Distrelec as a replacement for the broken board.
The Arduino.cc board works fine, but Distrelec sent another broken board. Looks like they have faulty boards in their stock.
I compared the two boards, the PCB layout seems to be the same, the board color and silkscreen print look the same. So I think counterfeit can be ruled out. The only difference between the boards is the opamp IC4. The orientation of IC4 is different and also the device marking is different, it's "74TI R5R" on the Arduino.cc board and "K170 Y740" on the Distrelec board.
I emailed Distrelec and asked them to check their stock.
And I also emailed Arduino support again because the board's layout does not agree with the Eagle files they provide on their website. I asked if an updated schematics diagram is available.
Best regards, Christian