OK, I've been following this post for months, the post you agreed with is the first I can recall that actually seemed to technically identify the problem.
But I wanted to test what that poster has said. So I spent $4 on an exif viewer, and took a series of pictures, emailed them to my mac, and looked at the data.
I found an old post that SEEMS to describe how the EXIF orientation tag is supposed to be used.
http://sylvana.net/jpegcrop/exif_orientation.html
The tag is a number from 1 to 8, describing the orientation. The post shows what the letter F would look like with each orientation.
Back to my photos. I took 4, starting with the phone (IPhone 5) in portrait mode, volume on the left, and rotated right 90 degrees for each photo.
1) Volume to the left "portrait", EXIF tag was 6, the letter F would be lying on its left side.
2) Volume on the top "landscape", EXIF tag was 3, the letter F would be upside down.
3) Volume on the right, EXIF tag was 8, the letter F would be lying on its right side.
4) Volume on the bottom, EXIF tag was 1, the letter F would be upright.
Based on this, (and assuming the iPhone or my email (Mac Mail) did not change the EXIF tag, I have to say I think Apple has it WRONG!
What this is saying to me is that when the phone is held with the volume buttons down, it is tagging the photo with a 1, indicating that software does not need to change the orientation. Which is the exact opposite of what I would expect.
All you more technical people, please correct me if I am wrong, but I would assume that if the tag is 1, this is the default orientation of the camera. Can't tell if the portrait mode is correct, because I don't know what the unrotated photo orientation is. Part of me says that with the home button down, that the tag should also be 1, but this assumes that the camera changes the location of the "top/left" pixel when you rotate the camera, which may not be true.
Hope this helps.