Kim, I certainly couldn't fault those fitters for being safety conscious, but if I lived somewhere that needed that level of precaution, I'd be very concerned.
The dangers are very real. We've got an open log-effect gas fire in the lounge, and of course we don't want bloody great venting floor grilles sticking up through the carpet. On a very cold night last winter, we left the fire on and we forgot to open one of the windows for ventilation. And yes, we both (wife and me) fell asleep on the sofa. And when we awoke, our pet cage birds were all dead. Another hour...
I strongly suggest you get a few battery operated carbon monoxide detectors. The Gas Company will supply them. Put one in each room.
Cheers, Steve