There's a lot of wrong stuff in that article.
First, it assumes that digestion is perfect. But let's roll with that. The article states that food is "almost totally digested by the time it leaves the duodenum". This leaves the entire stretch of the duodenum available for undigested food particles to cross. So this alone is no evidence against the so-called leaky gut theory.
Second, intestinal permeability is a very well known phenomenon, and has been extensively studied in athletes (vigorous exercise increases permeability). It has also been studied in cases of microbial enteritis - infection of the gut with pathogenic bacteria, fungi, or viruses. Endotoxins and exotoxins produced by infecting bacteria have been observed to cross from the intestines into the bloodstream, where they cause a variety of symptoms. These toxins are often full, undigested proteins.
The article neglects to realize that it doesn't matter that there are "several layers of cells" separating the intestinal lumen from the bloodstream. Proteins are tiny. The spaces between cells are larger than 1 protein. In fact, there are proteins called selectins, cadherins, and integrins that project into the intercellular spce and interact with other selectins, cadherins, and integrins to hold cells together. Depending on how many there are, the interactions between the cells can be tighter or looser, and thus permeability status can change, as is seen after a period of intense exercise.
Moreover, you don't even need a full protein to incite an immune response. You can have a protein fragment - say, 30 amino acids - that can induce a potent immune response. And since food is still undigested in the duodenum, there are plenty of opportunities for a 30AA fragment to cross into the bloodstream.
The authors of this article also seemed to forget that entire cells pass through blood vessel walls and the walls of the intestine depending on the composition of their surface proteins. How else would macrophages get around?
Antibody testing is a bit of a different story. IgG4 indicates downregulation of an overactive immune response - tolerance. Many food sensitivities look at IgG, and in particular IgG4. People get confused when they get their results back, and see high IgG for a whole bunch of foods that they didn't think caused them problems. And they're right - most of those foods don't cause problems, because a high IgG reading is indicative of tolerance, and not intolerance. However, there is another takeaway from the IgG tests. If you have high IgG antibodies to a certain food, that indicates that an immune response did happen, but is now being controlled. This can be indicative of a related problem. For example; if you come up sensitive to wheat and chocolate, the wheat could be causing damage, thus allowing other molecules to cross into the bloodstream and react. Your problem isn't chocolate, but rather the wheat, even though both come up as problems on the IgG test. It's also possible that a microbe is increasing permeability, and food isn't a problem at all; once the inflammation is dealt with, the problems go away. There are many of these scenarios that are possible, and it's extremely difficult to figure out which one if happening for you.
But what is NOT true is the idea that IgG antibody tests just don't matter. They matter. They give you information that is useful, and can indicate a problem. It is merely difficult to identify the root of the problem.
It's also important to note that the immune system interacts different with particles in the bloodstream as opposed to the lumen of the intestine. There's an interesting study somewhere that explained it nicely. I think you can find it on the wiki page for IgG if you're interested.