The rubber dams do go over the tooth but as a patient it feels like it is right under your nose. I couldn't smell the rubber when I had one on. They put it over my tooth on a frame then they cut the bit that goes over the top lip and it is that bit that feels like it is under your nose which it is really.
The1701 maybe when you had one on before they didn't cut it to fit under your nose enough. I don't see any reason why they need to use one for a filling. As you have to give your consent to have one put on then say you want the filling but you do not want the dam on and explain why. If they still would like you to give it a go then if you wish you can agree to try it on the condition that they will remove it if and as soon as you ask.
They can be removed in a second by flicking something on the frame, it will take a couple of seconds to then remove the rubber from around your tooth.