This is an example of how lawyerly thinking differs from the general population. The lawyer views all human interactions as contracts, and thinks that the contract is defined by the fine print. A non-lawyer is apt to see such thinking as bizarre. A supermarket is just a place to get groceries, and a discount card application is just a form to fill out. There is no negotiation, and no balance between the parties. The supermarket doesn't say what it is going to do with the data, and would not be likely to share similar data that might be of interest to the customer.
Businesses are defined by market forces more than by contracts. A supermarket initiates a discount card program with full knowledge that no one has an obligation to provide personal info truthfully, and many won't. If it really wants to track accurately everyone who shops there, it can become a members-only shop like Costco, and verify the data. It doesn't. It wants the business of people who shop anonymously, and it wants the business of people who lie on the forms. Feeling ethically obligated to tell the truth on forms that are only used for marketing purposes is silly. Just my non-lawyer opinion.