I can only speak for Texas, but I suspect the answer for Florida is similar. Because Texas was originally a Spanish colony (then a Mexican state after Mexican Independence from Spain), Texas used Spanish measurements. The oversimplification is that varas were used instead of meters and leagues instead of miles/acres. Shortly after Texas became an independent entity in 1836, it entered into an agreement with the Untied States regarding the boundaries of each. The agreement stated that Texas state waters extended three leagues. It seemed that no one noticed that 3 leagues is 9 nautical miles. I doubt that it was done maliciously, because Texas continued to use Spanish measurements until public domain closed in the late 1890s.

When oil was discovered in the 1940s, the issue came up again. Basically it was a federal versus state issue. The US Supreme Court eventually ruled that Texas was entitled to water extending 9 nautical miles due to the original agreement.

ETA: As mentioned below, there were multiple Supreme Court decisions, legislative action, and a number of presidential vetoes. A major point in the 1960 decision was that the United States had honored the 3 league provision for more than a hundred years.