The manual is a little decieving. It actually means you need a common, (or neutral) to the c terminal. It needs the common to power the stat. Think of it this way. You can grab hold of the hot wire coming of the low voltage side of the transformer and not get shocked, but if you touch the hot wire, and the neutral (common) wire at the same time, you will get shocked. Kind of like you could run one hot wire to a light bulb, but it won't work without the neutral wire also. Basically, your specific thermostat requires a true 24v to operate the themostat itself. It is not just acting like a light switch, which would just send the hot back out, but needs the neutral to power the stat. As for adding a terminal at the transformer, you would just cut and strip the wire and wire nut it together with an extra wire to run to the stat.
Most trasformers are labeled with a 24v wire and a common wire on the low volt side. The 24v doesn't do any good without the common. If you jump are to c, you will damage the stat, as the c terminal is not actually looking for 24v, but needs the nuetral to create a true 24v to power the stat.
The only other way I can think of to decribe this is to think of a car battery. A car won't start without both the pos and negative hooked up. Even if you jump the pos all over the car, it won't do a thing without the negative in place. Hope that makes sense. I really wish I could explain better. Bottom line, you need the common. If it were as easy as jumping are to c, I would save many hours and headaches from running new wires. However, nobodys is perfect, and I have been wrong before, so if you do find some literature, or someone who says you can make it work without the extra wire, please let me know. I'm always interested in learning. Just because I've been doing things a certain way all these years, does not mean there isn't a better way. Please let me know how things work out.
One last thought. Can you take the thermostat to a hvac dealer in your area and ask them their thoughts on this Let them know your situation, and see if they have any input. Good luck and take care.