As we know now, all generic user data and shared app data is stored in /storage/emulated/0. It is available for read and write access, but setting executable permissions for files located there is not allowed. The idea here is that the user won't be able to simply write to a disk and then execute a custom binary directly, even by mistake or as the result of a social-engineering attack.
In contrast, each installed app has full access to its own directory in /data/data, but not to the directories of other apps unless they explicitly allow it. This is done so that one app won't be able to affect the work of another one or get access to sensitive data.
