The the element is merely sitting on the line-height and not being positioned. So no, I think you are incorrect on that one. It is a nice bit of work otherwise.
It would be as if I wrote a tutorial on how to make one element fill the entire viewport, and one of my methods was "put all your content in the <body> tag" and I said that was a way to fill the viewport. That is the trivial case, it's a degenerate solution!
Well, there you go. :-)
It's worth noting that the last example with margin:auto can be used for centering within any div that has position: relative (there's nothing special about the whole page). It also works for intrinsic dimensions, so you can center an image without knowing its size, see http://jsfiddle.net/jdudek/hfbnS/1/.
There are a few more useful techniques not covered by this article, for example:
* line-height + vertical-align: middle + display: inline-block (which allows you to center vertically an element with dynamic height)
* display: table-cell (mentioned by others in this thread, although without stating its disadvantages).
While I appreciate the effort, calling the article "complete guide to centering a div" is an overstatement.
I think it would be best to simply replace that example with what is essentially the last example, which is much more useful. This codepen[1] shows the markup within another div. This is by far my favorite centering method, although it requires a fixed or percentage height while table/table-cell does not. It also avoids some of the bizarre quirks of table/table-cell, so there are times when one or the other is the best method.