I'm looking at the schematic for the MKR Proto SD Shield and it seems there are two versions of the MKR Proto SD Shield. The older version has only the SD card holder. This is the version in the photos on the product page and for which the documentation is written. The newer version has a W28Q16 flash memory chip in addition to the SD card holder (similar to the MKR Mem Shield) and that the schematic and board files provided on the product page are for that version.
You're correct that pin 4 is used as CS on both versions of the shield for the SD card. However, on the new version of the shield pin 3 is used for CS for the flash memory chip.
So please look at your shield to check whether it has an IC on it next to the SD card holder. I attached a screenshot of the board file for the new version of the shield. U1 is the flash IC:
Please let me know what you find.