Medicaid is just paying the insurance, had you paid for the insurance the bill would be covered by said insurance. In effect the FBI is "double billing"
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Claims experience matters to future premiums. The insurance companies don't have to take losses, and everyone's premiums go up. The amount of the claims is the amount of the fraud. Alternatively, comparing to buying insurance is a logical falsehood- they went on Medicaid instead of being uninsured.
The vast majority of people who apply for benefits while earning more than allowable are doing so because they are desperate. They earn too much to be eligible for benefits, and at the same time do not earn enough to survive.
Survive? Sorry, that's absolutely false. What you mean is they don't earn enough to maintain the expensive lifestyle they've chosen.
I have complete sympathy for that, as do you, and I'd assume most frum people. But don't expect outsiders to be as understanding - no one outside the community would equate that lifestyle with basic survival.