You are correct, getExternalStorage
will return your built-in external storage. Unfortunately, as of Jelly Bean applications are no longer able to utilize the SD card if the device also has built-in storage as well as an SD card. You can try working around it through shell commands or hardcoding paths, but without root there is no reliable way to access it anymore.
This was just recently added the Android CTS, which all OEMs must comply with in order to use the Play store.
Compatibility Program Overview | Android Developers
Section 9.5 (pg. 34) of Android 4.3 Compatibility Definition
Device implementations that include multiple external storage paths
MUST NOT allow Android applications to write to the secondary external
storage.
Storage Options | Android Developers
It's possible that a device using a partition of the internal storage
for the external storage may also offer an SD card slot. In this case,
the SD card is not part of the external storage and your app cannot
access it (the extra storage is intended only for user-provided media
that the system scans).
Android 4.2 APIs | Android Developers
Saving data in a multi-user environment
Whenever your app saves user preferences, creates a database, or
writes a file to the user’s internal or external storage space, that
data is accessible only while running as that user.
To be certain that your app behaves properly in a multi-user
environment, do not refer to your internal app directory or external
storage location using hard-coded paths and instead always use the
appropriate APIs:
For access to internal storage, use getFilesDir(), getCacheDir(), or openFileOutput().
For access to external storage, use getExternalFilesDir() or getExternalStoragePublicDirectory().
No matter which of these APIs you use to save data for a given user,
the data will not be accessible while running as a different user.
From your app’s point of view, each user is running on a completely
separate device.