Federal agencies manage Supplemental Security Income and Medicaid rules. As a result, no matter the state that you live in, any countable resources impact your eligibility for both of these programs. An individual can't have countable resources of more than $2,000. Supplemental Security Income countable resources include "life insurance" and "anything else you own which could be changed to cash and used for food or shelter." The same is true for Medicaid. You lose access to SSI and Medicaid when your countable resources total more than the allowable resource limit.
In the case of a permanent life insurance policy, the cash surrender value is counted as a resource because you could always cash it in and then use the money toward food or shelter. Life insurance products that have no cash surrender value or borrowing options do also exist. As you suggested, policy ownership is an important factor in determining resources. If you're the current owner of the policy, you could transfer ownership into someone else's name so that it no longer counts as a resource.
That said, transferring or selling a resource can also make you ineligible for SSI and Medicaid. In some cases, transfer or sale of a resource can make you ineligible for SSI up to 36 months. Since your son took out the policy, paid the premiums and benefits ultimately in the event of your death, you might have little difficulty transferring it to your son or your daughter-in-law. You also have the right to appeal the Social Security Administration's decision by requesting a "reconsideration determination" by someone who wasn't involved with the original decision. If you're denied payments again, you have the right to appeal in a hearing and then also to an appeals council. Speak with an SSA representative or your case worker about these options or visit the Social Security Administration's appeals website for more information.
Keep in mind that you have only 60 days to file your appeal requests. Additionally, you should also talk with your life insurance agent. Your agent has likely dealt with this type of problem with other policyholders in the past and might be able to give you helpful advice on how best to approach the appeals process.