Both you and Nominal have missed the point. And HP is a good tool to describe why. I understand and agree with your definition of statistical orthogonality.
No, I acknowledged your point already, and believe this is more a disagreement about the relationship between orthogonality and correlation in statistics.
I already explicitly described that there are brand owners that do emphasize product quality, but that I do not believe this has anything to do with how I use the term "orthogonal" in statistics. That is, I acknowledged your point and agreed it happens, but insist that it has nothing to do with how I use the term "orthogonal" here.
To me, statistical orthogonality simply means that you have two variables whose correlation depends on completely extraneous things. Correlation is possible, but not necessary. Here, the key extraneous thing is brand owner intent. As customers/users, we do not have access to the intent, but we can estimate it statistically, and use it to estimate the quality of a given product. Note how this isn't modeling the brand–quality relationship, because there is only one particular brand involved; it is just using the brand as an identifier when estimating the brand owner intent for a particular product.
Perhaps I'm using the term "orthogonal" wrong; I could be, but I checked the terms I know in a dictionary, and it seemed the best match to describe the above. (It is exactly this kind of key term nuances and understanding that I have the most trouble with in English. When speaking English face-to-face, body language provides a lot of cues; when interacting in English almost exclusively with written text, those cues are derived from context, with very little data, and are easily misconstrued. Another term whose subtext/cues I have trouble with is "to emerge": before emerging, did that thing exist or not? Was it just invisible/hidden? What are the exact emotive subtext in comparison to "reveal", "create", "construct"?)
Now, above, by "as customers/users, we", I mean engineers and scientists and thing-oriented people as opposed to people-oriented people.
They are more likely to assess the brand by their emotive reaction to it, and thus are more likely to be swayed by advertisements (that work by associating certain mental imagery and emotions with the brand). They more often choose the product because of the emotions and associations they experience with the brand, since the product itself (if brandless) does not create any emotional response –– remember, they're people-oriented, not thing-oriented.
It is at one extreme of the scale where we get both fanbois and haters. At the other end of the scale, we have the brand-unaware nerds who cannot even remember the manufacturer of the device, but can recite their specifications at any time.
Obviously, most people are not either-or, but somewhat people-, somewhat thing-oriented, so their own experience and needs regarding the product itself means that persons approach to brands varies.
And that, in my opinion, means that observation and analysis of ones own behaviour and choices is important in understanding
why we do the choices we do, so that we can learn how to do even better ones in the future. Just commenting on others' is rarely useful, unless the behaviour is particularly notable.
It is also why talking shop, honestly, about the tool choices we have made, especially the errors in our judgement when choosing a tool –– or adopting the opinion or advice of a "big gun" ––, is so useful and fun to us more-thing-orienteds. If done with compassion and not antagonistic emotions.