Actually it still applies. In the US EMT-B certification is regulated by the individual state Departments of Health. Within that, there are regional differences. The training you get will differ wildly from state to state and sometimes within regions. If you read some of the posts here, you will see, depending on the system you work within, the skills you learn and the procedures you are allowed to do are very different.
In some systems, you can't so much as given an aspirin tablet without a Physicians Order. In others EMT-B's are allowed to do everything from Nitro to Combi-tubes, Glucose to assisting Paramedics with intubation.
I don't understand the documentation issue. If you wish to be considered a US citizen, can't you just pass the citizenship test and become an official citizen? I would think that would be a much more direct path to your end goal. Military medical training is very different from civilian training and are not always interchangable.