The manufacture also reserves the right to package a lower quality product. I've bought generic cereal that I'm sure was Kelloggs, most of the time I couldn't tell the difference - every once in a while there was a slight burnt taste. Still food safe, but not as high quality.
Because even though the product might be from the same supplier, it is not a product of this brand.
There is a big difference.
The customer-expectation of a brand-product is based on the perception, the history and the presence of that brand, a well-crafted association and experience that is funded with the profit of the product.
The private-label product is cutting this funding. It will not finance the supplier-brand and it sets its own expectation and quality-thresholds on the product.
The supplier accepts that and waives his control to get the volume-order and fill production-gaps in its factory.
In this kind of deal there is no direct relationship between the original brand and the private-label product anymore.
Edit, for clarification:
It's not said that the potato-chips will be exactly the same. The minimum requirements of the brands may not match with the minimum-requirements of the private-label, i.e. for the private-label a different grade of potato, oil, salt might be used.