Seems like you‘ve grasped the overall summary of oversight in the US pretty well. Additionally, Steve Savage’s response provides a great summary of the regulation of GMOs: http://gmoanswers.com/ask/how-are-gmo-foods-regulated.
“Working with the broader community of academic and commercial scientists, three US regulatory agencies hammered out a system of shared responsibility for the review of biotech crops. Called the “Coordinated Framework for Regulation of Biotechnology,” the system was instituted in 1986 – still 10 years before the first commercial acre was planted. The proactive involvement of three regulatory agencies is completely unprecedented making crops improved through genetic engineering the most carefully monitored foods in history.
The USDA considers whether there are any “plant pest” issues with the specific crop and trait such as the ability to cross with weedy relatives. The new crop cannot even be planted outdoors for testing purposes until the USDA determines that it is prudent to do so. The EPA gets involved if there is anything pesticide-related to do with the trait such as tolerance to a herbicide or the production of the Bt protein that protects the plant from insect damage. The FDA reviews the information that the producing company or other entity generates to show that the modified crop is “substantially equivalent” to the non-modified version. This step is technically voluntary, but that sort of data has been provided and reviewed for every biotech trait that has been commercialized in the US. The exact nature of the equivalency testing is, logically, customized based on the type of trait involved.”