That link doesn't work for me, says request not found.

Can you clarify this a bit? I.e what does the Dropbox app do if you take a picture in portrait mode, and what does iOS do? Is the rotation info lost completely?

Yes: it rotates the pixel data and resets the EXIF Orientation header. That means that it looks identical even when displayed as expected with a viewer which doesn't honor the EXIF orientation.

It's a lossless rotation - you can actually use something like jpegtran to rotate it back and the pixel checksum in ImageMagick's identify will match – but it completely breaks any system which uses checksums to detect duplicates, of course. I noticed when I started testing Google Photos and had a ton of duplicate images.