You don't take the data at face value. The goal of these systems is to reduce human intervention, not to remove the intervention. If a firm fakes data, you still have proof in the bad products and customer complaints. This lets you investigate and file complaints on the public blockchain. Think of it like a review of a company's supply chain reliability.
More advanced systems consider using third party, tamper proof scanning systems and packaging. Again, the costs of these systems are quite high, especially for food, but there are physical ways to reduce fraud if the data holds enough value.
They can always print fake labels, but they can't deliver fake products too many times. Customers will realize that fraud is happening. Again, there are also ways to make labels that cannot be faked, then attach those labels to tamper-proof packaging. It helps to realize that these labels and packaging exist so that the food items can be scanned and tracked as they enter and leave different facilities along the supply chain.
A blockchain is useful as a review database because you have guarantees that the reviews came from the claimed reviewer. This reduces fake claim fraud, which you might, for example, see in restaurant reviews. The reputation of the purchasing company is also at stake when they make claims that another company committed fraud. You want good guarantees that information came from the party it's ascribed to. It's reputation building in a scenario without mutual trust.
More advanced systems consider using third party, tamper proof scanning systems and packaging. Again, the costs of these systems are quite high, especially for food, but there are physical ways to reduce fraud if the data holds enough value.