Would you die with your pets of they could not be rescued by you or others?

Some years back when there was one of those sever hurricanes headed for Florida, I seen a news show (could have been Nightline) where they were interviewing some of the people who did not flee but were trying to stick it out. I remember one woman was saying because they had too many dogs, and had no place to take them, as they could not take them to the shelter the government, or those working with the government set up, they were sticking it out in their home; they were not going without their dogs. She said something to the effect that if their dogs had to stay there and die, they would be with them (the dogs). Would you die with your pets even if you could be saved but your pet (dog, cat, pot belly pig, horse, etc.) could not?