You are absolutely right.
One summer I worked part time in a major food processing plant (tomato products). I saw as many as four different store brand names come off the same processing line.
I talked to a food plant management guy many years ago and he laughed at the idea of different brands of tomato sauce, he pointed out that it is a farm region product delivered by the truck loads and an industrial food plant, he said that they gear up to make and can sauce by massive volumes and that the only thing that changes in the process, is glued on labels.