When you think about it, it's really quite simple. Even though you have a valid cert, you still need to be under a medical director to be able to operate as an EMT. You can't just run around with oxygen, glucose tubes, an AED, a couple of epi pens, ntg, or albuterol w/nebulizers on your own without medical oversight, can you? That would be illegal.
When a medical director authorizes you to operate as an EMT, you can then consider yourself one.
Another way to think about it - when I first got my medic cert, I was still an EMT until my hospital's OMD signed off on me to operate as a medic. In the interim, I was just a card holder. If I were to have dropped a tube, paced, pushed meds, etc. to "help out" it would have been illegal.
The cert grants you authorization to operate under the OMD's medical license. When you're signed off, then you're authorized to operate within your scope. Then you're officially an EMT.
If I were to quit my job tomorrow I would be an unemployed individual with an EMT-P certification. I'm not a paramedic because my cert is useless without proper medical authorization.
Edit: The reason I'm harping on this is because there are individuals out there (whackers) who will "reappropriate" (steal) medical equipment, such as O2, glucose, epi pens and such and freelance on their personal time. One poster was even asking about carrying around their own personal AED! I've seen medics that carry around their own intubation set, along with IV equipment, IV NaCl, admin sets, etc. This is for off duty use (abuse), which is way different from being authorized to practice off duty in your district, if such a provision exists.