Apps are supposed to ask the user (just like Amaze does if you try to modify a file on SD card). It’s also possible (with root) to circumvent this by using adb to pull /system/etc/permissions/platform.xml from your phone :
adb pull /system/etc/permissions/platform.xml
edit it by turning
<permission name="android.permission.WRITE_EXTERNAL_STORAGE" >
<group gid="sdcard_r" />
<group gid="sdcard_rw" />
</permission>
into
<permission name="android.permission.WRITE_EXTERNAL_STORAGE" >
<group gid="sdcard_r" />
<group gid="sdcard_rw" />
<group gid="media_rw" />
</permission>
then re-push it to your phone
adb push platform.xml /system/etc/permissions/platform.xml
Then reboot your phone. You might have to adb remount
before you push though.