Walmart, Amazon, and the other big companies are not interchange exempt. They are not able to get a significant discount below interchange, hence why they keep financing lawsuits against Visa, MasterCard and such over the bundling of all Visa or MasterCard branded low-cost (non-rewards) and high-cost rewards cards under one banner that they are forced to accept as a bundle.

Merchants would love to reject all cards that are a Visa Signature and above, leaving only the very low cost cards as accepted. The Card Networks have engineered via branding and contracts that this does not occur though.