What, exactly, is nonsense about it? I don't see anything obviously out of place with the
comparison between the two lenses.
What's 'nonsense' LOL is that when you bring up the test images, the 18-55 looks sharper than the 18-55 2.8 (which costs six times the price) when in real world picture taking it is not.
Everybody knows that it is not. I have both lenses myself. The text of that review refers to the fact that the target shots don't do the lens justice, because of a combination of factors. From memory I think they speculate that the 2.8 lens is optimised for longer shooting distances and that is almost certainly a factor.
But the other thing, that they do not draw attention to, is that even if they used the largest of the three target sizes available, at 17mm they are shooting it from only 1m or so, and the edges will be at least 20cm further away than the centre. While manufacturers strive to keep the focus field of the lens reasonably flat, this is not a very important consideration in practice - unless you shoot 2D test targets from very close distance. So they quite often let this factor drift a bit in the best interests of making the lens perform really well where it matters.
Basically, if you take a real world situation, like a 3D subject shot from maybe 3m or more distance, then the 17-55 2.8 is scalpel sharp all over, and sharper than the 18-55 IS, as you would expect. As well as being f/2.8 throughout. This is the experience of everybody who has this lens, and why we are happy to pay the premium (not forgetting very low distortion, good vignetting control, and higher build quality etc).
The problem thay have is trying to get a test that is simple, easy, cheap and repeatable to do, and can cover lenses from super wide to mega telephoto. That is a very big ask and unfortunately, no such test procedure exists. The manufacturers use computer generated MTF tests, with the lens focused on infinity, and at huge cost, but this comes out as a not very user-friendly set of graphs. There are plenty of them to be found on the Canon site though, even if what they ultimately put out only gives a small glimpse of overall performance. Nikon and Sigma also publish comparable MTF graphs.
Edit: here are the Canon MTF graphs. As far as I can see, there is nothing to choose between the IS and non-IS versions of the 70-200L 4.
70-200L 4 IS
http://www.usa.canon.com/consumer/controller?act=ModelInfoAct&fcategoryid=150&modelid=14260
70-200L 4
http://www.usa.canon.com/consumer/controller?act=ModelInfoAct&fcategoryid=150&modelid=7345