The apps only have access to the SDK API functions - I know Sandisk can read from the Lightning port so the app itself can read all the contents on the drive - it's a matter of developing an app to read from the port itself. I believe you'll see more apps implement this real soon since this USB 3 Camera connector is released!
Love to hear if you do decide to look into it. I was always under the impression that it wasn't as simple as this though. Since Apple hasn't released a way to talk to the device, it's not possible for apps to read from it. The other devices, like Sandisk, use their own hardware with their own code to talk to that hardware. Without the API being public it's very difficult to know what the device is expecting.