There's an additional "post processing" step that the article doesn't mention -- which is alignment of the images within the wiggle.

In the example images (which others have noted are stable horizontally) - This alignment gives some control over the parallax and has a very big effect on the quality of the 3D and the ultimate experience of the image.

If you put your mouse, for example, over the marlboro pack that is most directly facing the camera, you'll see it is perfectly stable relative to the screen (despite looking like it's wiggling). In the second image, this point is at the eye of the singer.

On the accidental images, which are also mostly not stable horizontally, this type of alignment can also have a very big impact. An extreme example of how this plays out can be seen in this image - which for example -- locks onto the face

https://strickgifs.tumblr.com/post/48624241536

(NB - like 12 years ago I used to do make a lot of wiggle images -- including spending some time making wigglegrams out of a set of 3D images of the 1906 San Francisco Earthquake & Fire -- https://thesanfranciscowiggle.com/)