This answer does not address the exact case in the link you gave, but it provides another way of hiding data:
It would also be theoretically possible to hide a file within the JPEG picture itself, but you would need a complicated program to write the encoded data and then read it again.
Basically, a JPEG photograph contains a lot of information which, if it changed, would not be noticeable to the human eye. Imagine you have a photo of a person in a blue shirt. If you zoom in on that shirt you will see that it is not an even blue colour, but made up of a multitude of flecks of colour, most of which are a bluish tone (but some could be other colours as well). You could easily change some of those flecks to a slightly different tone and it would make no obvious visible difference to the picture.
A clever program could embed a code in the photo by subtly changing pixels to a pattern that represents data. A very simple example: if the "hue" (i.e. colour tone) is represented by a number between 0 and 255, pixels of an even hue could represent a "0" bit and pixels of odd hue a "1" bit. It would be hard for the human eye to detect such a difference in the picture.
It is an old idea and this article discusses how much data could be hidden in this way: High capacity data hiding in JPEG-compressed images (2004)