NJS,
You're probably both right and wrong, depending on the state, but I also think you're missing the point of the question, which was, "how do I get training" not "how to I work as an EMT."
I know of a few states that require you to affiliate with medical control and maintain that affiliation to get your Paramedic card, so it's possible that the same situation exists for BLS techs as well in some states.
However, that's not the point. Being an EMT does not allow me to outfit my minivan with lights and sirens and call myself an ambulance. It does allow me, with the appropriate medical control, to work on someone elses ambulance, but the ambulance would not exist without the medical control, so I don't really worry about it all that much.
Being an EMT also gives me the skills to help out when I'm not working under medical control. When I tended to a woman having a seizure at 35,000 feet on a transcontinental flight I was a passenger on, I was not acting with medical control - I was a good Samaritan who answered a call for help, and I was protected from liability by good samaritan laws.. Similarly, if I stop at a car accident while driving with my family (which I have also done) I am protected by good Samaritan laws, as long as I follow my training and protocols.
So back to the original question. I have already suggested volunteering with your local fire department or ambulance company. Other places to look are community colleges for courses you want to pay for, and the always popular WEMT certification. CERT and the Red Cross are good for basic first aid, which is certainly useful, but not as involved, and will not give you the same comfort and experience as working an ambulance will give you.
Sorry for the long post!