There is no evidence that OLEG OLEYNIK, the "expert" who is credited with being the author of the article you wrote, exists. It cannot be proven that someone doesn't exist. You are the one implying this person exists, and it would be VERY easy to provide evidence that such a person exists. All searches I have performed either link directly to the article you linked - or to a forum discussing this article. There is no other mention of this person, so unless you have something I haven't seen, assuming the person does not exist is a fair conclusion to draw until you show otherwise.
As for the claims made in the article, as someone has pointed out, they are nonsense. It is impossible to draw such conclusions because in order to make a REAL comparison of distances using parallax, the camera orientation of each photograph must be known, and the exact distance between each photograph must be known. Neither is provided anywhere in the article. This way you can rule out or isolate things like barrel distortion of lenses. In the comparisons made, it is very likely that parallax cannot be measured at all because the photographer didn't actually change positions between shots; he merely panned the camera to the left or right from the previous photograph. We don't know. The article does not say (nor did NASA keep such records of precise relative locations between all shots unless they were specifically for 3D compositing - which none of the photos in the article were to my knowledge). You're not going to be measuring ANY parallax in the event that the photographer did not move between shots, but merely panned. The difference in tha background in tbat case is due to the background being in a different portion of the image circle, and therefore subject to varying degrees of barrel distortion - which is something that occurs on ALL lenses to some degree, and the article does not mention the lenses used nor the effect of barrel distortion on that particular lens. No mention at all that it's even a consideration. Something an "expert" would most certainly include in such an article.
Furthermore, at one point, the article compares two images that are KNOWN (and acknowledged to be IN the article) to be taken out of a series of panoramic shots. This is where you would stand in the SAME SPOT, and simply take a series of photos while basically spinning in place. Panning a little farther each time. There will be no difference at all in the background between two frames OTHER THAN barrel distortion. So the article is comparing two images that are KNOWN to be taken from the exact same location; just panned slightly differently, so it should have been KNOWN to the author that the ONLY possible explanation for the difference in backgrounds between two pictures taken from the SAME location is due to barrel distortion of the lens. The author makes no mention of this as even a possible cause, when it is in fact the ONLY possible cause because there is no parallax to be measured in two photographs KNOWN to be taken from the exact same spot - just panned differently.
It's all nonsense. It's an excellent demonstration of someone blatantly butchering well-known concepts, and of course those who want so badly to believe that the landings were faked who know NOTHING (and in your case, ADMITTEDLY nothing) about the science involved get mesmerized by the complicated-sounding notions, and just fall so easily for them.
TL;DR : There are no conclusions to be drawn from the analysis of the photographs regarding parallax because the author has left out information that is critical to the analysis (orientation of the camera; exact distance between the two vantage points). In at least one analysis, the author compares two photographs the HE ACKNOWLEDGES came from a panoramic series, which means the photos were taken from the same location; only panned differently - in which case there would be no parallax, and the only explanation for the distortion of the background is from the lens of the camera.
A proper parallax analysis would include the lens used - analysis of the lens so that barrel distortion could be eliminated or isolated, orientation of the camera when the photographs were taken (relative to each other) and the location of each photograph (relative to each other). None of that is done. It's literally a guy who understands nothing about parallax layering two photos on top of each other, and saying, "Look at that!!!". Make up a name, and put "P.H.d." behind it, and people like you just fall to pieces over it.
Nonsense.
If this person exists, it would not make his article any more credible. It's still nonsense for the reasons above. The point is just the lengths some hoaxers will go to propagate the hoax. If the person is real, I'd be surprised if his credentials have anything to do with parallax. At best, the argument is an appeal to authority. And that's the best you could possibly do. You'd have to prove the guy's existence just to be upgraded to "fallacious argument".