Botulism wasn't the cause of death because the ashes provided evidence that they cooked their food which would have destroyed the toxin. Mother covered face - pimples start on face. Botulism is impossible because they had fire available to heat their canned food and this would destroy the toxin. Cowpox is a threat to those who milk cows and there were no cows around. The plague is not the cause because it is highly contafious and many more would have had it.
Smallpox is the cause of the deaths.
Sarah and Yates were allowed to take care of those in the quarantine tent because they were immune to smallpox. Yates had a pockmarked face and Sarah was allowed to go into the tent after her arms were examined. They must have shown evidence of pock marks, too.