Two points:
Firstly there is a list of those medical conditions that a passenger is not allowed to board an aircraft with because of the possibilty of their being contagious to the other passengers. These will usually include relatively minor ailments such as chicken pox to the most serious ones such as open tuberculosis of the lungs. No doubt SARS has been added to these lists.
Secondly it would be most unusual for the air in the cabin to be changed every three minutes. Most aircraft now recirculate the cabin air through some pretty inefficient filters and only take in a percentage of fresh air to maintain the cabin pressure. Have the airlines in question given a guarantee that the "re-circ" fans will be switched off thereby ensuring clean fresh air is indeed, circulated?
Now consider the problem of passengers who board not realising that they are infectious and also that the cabin air is recirculated.
It may not be a healthy situation but the risks are still minimal and probably less than the risk of contracting malaria on the way to the airport!
Nothing in life is without risk, but switching off the recirc fans when operating in certain areas would seem a good idea.