People who are applying for Medicaid eligibility should likely not be carrying any kind of private insurance. If you are able to afford a form of private insurance they likely have too much income in order to be eligible for Medicaid. Private insurance can be very expensive. If you are able to afford private insurance, you can rest assured that in most states you will not be granted Medicaid eligibility. A person who is a social worker should be able to catch the fact that a person with private insurance is trying to become eligible for Medicaid.
Many states out there may be struggling with their Medicaid funding formulas already. These same people who are working for a given state do not need people committing Medicaid fraud by having private insurance and still applying for Medicaid eligibility. If you have health insurance, you should not apply for Medicaid eligibility. The fact that wealthy people would try to scam the system is only a way to drain resources from the system. This means that poor people who actually need Medicaid will have a harder time obtaining it. You need to not apply when you already have health insurance.