I didn't go to the link, but I have read other sources that agree with the basic idea you outlined in your post. I disagree with you, I think it makes sense.
I didn't say anything about whether or not I think it makes sense. I said that I haven't seen any medical or scientific support for the claim they're making. BTW, I posted a message on that same site, asking them if THEY know of any scientific evidence for their claim. Let's see if they respond to my challenge. I'm not holding my breath while waiting for them to respond!
I think that if your skin is very tight, flaky, and/or painful to move or stretch (i.e. it hurts to smile), but within a few hours becomes greasy, it would be reasonable to conclude that your skin is compensating for the dryness.
I suggest that you not always assume that some idea or theory is necessarily
correct, just because it may seem
reasonable to you. There are a great many theories in science that seem reasonable at first, but turn out to be incorrect.
I have found that applying a moisturizer or humectant of some sort alleviates this "compensation oil" effect- unless, of course, the moisturizer you choose is applied too liberally or is greasy and unabsorbent in nature (such as Vaseline).
And how exactly did you make the determination that it relieves the alleged "compensation oil" effect? Please be specific.
I personally did a careful test on myself nearly three years ago which had a completely different result from what you would expect, and I tested it in a scientific fashion. I washed my skin very thoroughly with Ivory soap 5-6 times a day for several days, and as you can imagine, it got VERY dry and very irritated. But despite that extreme dryness, there was no change in sebum production at all. And by the way, I measured my sebum production (both before and after the series of washings) with Sebutape test-strips, which is a scientific instrument used by doctors and scientists for just this purpose. If you want to read a detailed description of the way I conducted the test, and even see scans of the actual Sebutape test-strips from the test, see my thread "FINALLY: a more direct test of the 'feedback theory' ", which you can find in the Acne Research forum.
That's how _I_ did _my_ careful test, which showed no "compensation oil" effect at all. Now let's hear how YOU did YOUR test!
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I was actually just sharing my opinions, based on my experiences...I didn't expect such an enlightening response

You definitely have the scientific advantage here. I'm simply seeking from experience. When my face is dry, tight, and flaky after washing (and becoming shiny later in the day), I apply moisturizer of some sort (homemade, storebought, oil free, straight-up oil, glycerin...). Oftentimes my face will become softer and less greasy.
The problem with my experience is that I don't know what my true skin type is. I began using harsh acne products (like 10% bp) around age 12, when I first began to get occasional noninflammatory acne. I have often wondered if the products and/or their residue on my skin caused the shiny appearance, and my skin is not truly oily (this would explain why it feels dry after washing, and oily later in the day after I have topical acne treatments or makeup on). It could be my makeup that is causing the shiny, oily feel on my skin. I'm not sure.
Your test seems very interesting, and and I may even change my skincare routine if you can help me figure out this conundrum. How do you suggest I figure out what my skintype is? Actually, how do I know that my skin is inherently oily, rather than oily because of product residue? If one has oily skin on their face, I would assume that the oil glands over the rest of their body also produce more oil than those of people with "normal" or dry skin. Well, I have quite dry skin over the rest of my body, and my hair is
incredibly dry (indicating the condition of my scalp). Can you shed some light on this?
Thanks