Was having this exact issue with both of our EX3’s here at our rental house.
Called our Sony engineering line and spoke with one of the techs.
After telling him that I had done the FB Adjust under proper lighting, etc. he asked what firmware version I had. Oddly enough, one of them had v1.02 and one had 1.05.
Sony’s most current version for the EX3 is v1.1.
After he stated that upgrading my firmware would clear the back focus problems, I could upgrade the camera myself. But, only the camera with version 1.05 (user upgradeability unlocked at v1.05).
After a tricky process of upgrading, from a hidden usb port on the bottom of the camera, and doing the auto back focus adjustment test again, the problem has been cleared.
Hope this works for everyone else….
If you have v1.05 or later you can get the download here:
https://pro.sony.com/bbsc/ssr/micro-xdcamexsite/resource.downloads.bbsccms-assets-micro-xdcamex-downloads-XDCAMEXFirmwareUpgrade.shtml