The thing with the food stamps is that the system can be setup like that because of the negative social stigma attached to social welfare programs and the fact that people self-regulate when it comes to accessing those services.

It doesn't really need to be fixed until and unless it is shown that people whom do not need these services are taking advantage. A single wealthy person doing it to make a point is not a systemic problem. If that person's actions then motivated hundreds or thousands of otherwise well-off people to collect on food stamps, then it'd be different.

The fact that those programs are so easy to access is part of why they work at all. Poor people whom need that help may or may not have proof of identity, proof or address, a bank account number, etc. Forcing people in need to prove things like that undercuts the ability of that public service to work.