I don't have an S3 so can't check directly, but the usual thing is that the marketing people quote the total storage capacity of the phone, but fail to mention that part of that has been allocated for the system software and so what's available to the user is actually less.
There's also the infamous digital vs binary units scam. Computing devices use binary units, so 1 GB = 2^30, which is 1.074 billion bytes. A decimal Giga is 1 billion. So storage device manufacturers quote the capacities in decimal units because it makes them sound 7.4% larger than they really are. That's why a 16GB microSD only actually has 14.9GB usable space, and I imagine the phone makers use the same convention.
So my guess is that Sammy have allocated 3GB for system files, which then leaves 12GB for the user.