LC, it is you who continues to ignore the point. NYS law doesn’t give a hoot that they consider themselves married and present themselves as being married. They used Halacha to make sure their relationship was kosher. NYS law requires that they claim to be single for purposes of filing taxes, SS benefits, pensions, etc. NYS law doesn’t even allow them to claim to be married for those purposes. If such a couple claimed to be married they would be breaking the law.
Avi, Federal law doesn’t purport to determine whether someone is married or not. Federal law uses the State to determine whether anyone is deemed married or not. For the purposes of Social Security and SS only, the law you cited above does seem to hold that if they publicly present themselves as husband and wife then they are deemed to be so for SS purposes even if they are not under State law. This would affect SS but not pensions or other instances where it matters whether the party is married or not.