It was not as though Imogen was squeamish, more that she did not want to cause offence. Every one had to die at some time,and many people recognised this. Well, recognised it in theory. Recognised it in others. However, when it came to their own death, most people turned a blind eye, or a deaf ear. However one looks at it, people simply could not recognise when their own demise was nigh.
Jack was close to death. He was dying. Actually, the other way around: close to death is closer than merely dying. Dying is still in the back straight, whereas close to death is within bull's roar of the finish line.
Jack was so close to death, his skin was sloughing, and his eyes full of eternal light, yet still he would deny it.