I remember a friend in the know who said 'own brand' products are often just re-branded and made to look cheap and tacky although it's the same stuff as premium brand.
Urban Myth!
A reputable "brand" may very well make supermarket own name products. They do, however, vary the recipe or dilute the product to ensure that the difference remains.
Different supermarkets also have different "recipes". For example, a well known Dairy firm makes "Custard Flavour" yoghurts for the leading supermarkets. Tesco's offering is watery and the two fruit flavours (apple and raspberry or plum) contain fruit pared very close to the core. The Waitrose offering is thicker and creamier with four flavours offered, the pieces of fruit used being much fleshier and without the hard bits of apple close to the core (seed cases) that cut your gums.
This is the reason why Waitrose own branded merchandise is consistently of high quality while Tesco, Asda etc is "hit or miss".