I have heard this statement so many times more often from people with anti-capitalist, socialist, or post-modern attitudes. (Yeah, I know, these aren't the same terms, but you know what I mean.)
Such a statement is contradicting with the human nature of trying to avoid loss and hence evade risk. Also, there is a contradiction between action and word here in a sense that you are paying much less for a non-brand product while you should pay the same price should you really not care about brands!
When you buy a product, you don't just buy a piece of physical material or an intangible service. You typically buy a package, at the heart of it is the product, but it's not limited to that. The package extends from the moment you decide you want something at time t-1 to the moment you are transferred with the product at time t, to many days, months, or years thereafter, which we can denote as t+1.
In such a process (t-1, t, t+1), you want to have control over the parameters, which affect the involved variables. In an indirect way we can say, you pay for information.
Brands are in a sense credible sources of validated information. You value them because of exactly that, and you are willing to pay for it. You pay for integrity of their PR activities + their corporate social responsibility + their quality products + customer service + ... and you pay because you are certain of these values. Brands are credible.
In absence of such credibility, you are taking risks of incurring losses, hence you make a compromise by reducing the price you are willing to pay for a non-brand product.
Let me make an example with used car market though it's not exactly brand and non-brand but it should establish the point, which isn't really about prestige or other probable factors to valuing brands more. The price of used cars aren't for example one-fifth of the same cars that are new because they are performing bad. The reason you are willing to pay a much lower price is because you don't know exactly what losses you are incurring by buying such a car. There is an "asymmetric information" level about the used car between you and the seller, so to speak. (This is also referring to the "Law of Lemon.") There is no credibility.
I don't care about brands, either, but to a point, where I can afford incurring a loss.