From my personal experience with BA (on two seperate occasions), I have no doubt that if proof of illness had been submitted the Station Manager would have accommodated them without penalty. You must understand that airlines are continually confronted by pax trying to bend the rules for no better reason than that they simply want to prolong or shorten their vacation. It is therefore only right that airlines seek some form of proof supporting the claim. Therefore, if you have to change plans because of illness, inform the local Station Manager immediately and obtain a note from the doctor.