Means testing in social services is such a terrible idea. It creates nothing but perverse incentives like you describe. Programs like food stamps should be available to everyone who wants them. I don't care if a billionaire uses food stamps, they still need to eat. If too many rich people use the program, tweak tax rates until it balances out.

It's a waste of our time to go through and double check that only those that 'deserve' a handout get one. It makes everything less efficient, creates bad incentives, and builds a social stigma around the programs. ("Oh, that program is only for really poor people. I'm not really poor, so I shouldn't use it.")