FWIW, I researched this about a year or 2 ago, and found articles saying his mother, Oriales, had become a citizen years before her husband. I looked for those same articles, but have no idea now where I found them at the time.
In looking, I found a number of articles indicating that the timelines had been updated since last I looked. They are indicating his mother became a citizen in 1975 at the same time as his father. That being the case, your position has merit.
Were I to view this differently it would be based on the nation’s earliest naturalization laws (1790?) that would have coincided with the 18th century understanding of what becoming a citizen at that time entailed. As I recall, it was 3 pronged:
1. 2 years residency
2. Appearance before any magistrate
3. Oath of allegiance.
I believe his parents arrived in the US in the neighborhood of 1959-61 to stay. During that time, it appears they did appear before the legal system for permanent residency, maybe more than once. The only question would be the type of oath required for permanent residency and how it compares with the 1790’s oath. They had clearly met 1&2 before Marco’s birth in 1971.
The U.S. Government did not have a Federal immigration law until the mid-19th Century, because the sovereign States determined citizenship law instead of the Federal Government. New Jersey's citizenship laws treated the citizenship of women more favorably than most other states in 1787-1800. Upon the Federal Government adopting uniform immigration and naturalization statutes that superceded the State naturalization laws, who could naturalize as U.S. Citizens and how came under the authority of the U.S. Government. Before then, a person became a citizen of a State in accordance with State immigration and naturalization laws in order to become a U.S. Citizen.
In 1971, the immigration and neutralization law was the responsibility of the U.S. Government and not the State of Florida. Under the then existing Federal statutory law and the 14th Amendment of the Constitution, Marco Rubio had the right to claim U.S. citizenship upon native birth or Cuban citizenship at birth by the act of his parents until he confirmed or denied that act of his parents by accepting or rejecting his right to claim his natural born Cuban citizenship upon reaching the age of majority.
Another insuperable problem with trying to use an 18th Century, 19th Century, or 20th Century statute or Constitutional Amendment to confer or retract citizenship is the fact that such law is manmade and not natural inborn citizenship. Any form of native born citizenship can be altered by manmade laws. Natural born citizenship cannot be altered by manmade laws, because the membership in the community is determined by being born the child of two parents who are members of the community. While such a natural born citizen can forfeit or abandon such citizenship after birth, nothing manmade law can change the fact of nature. All forms of statutory citizenship from naturalization to native born citizenship to alien parents are the artifacts of manmade law, which can be changed by man by changes in the laws. All laws employing jus soli to confer citizenship are examples of manmade laws making the child a citizen, rather than the child being the natural inheritor of the parents’ citizenship and membership in the community. Reliance upon the 14th Amendment and/or immigration and naturalization laws to determine citizenship precludes the possibility of a natural born citizenship.