I can definitely see that they are being rather irresponsible in asking you to come to the airport after you declared the possibility of being infectious. That seems to be unjust towards the potentially genuinely unwell passengers and also other passengers who may get exposed to the virus.

Encouraging people to fly when potentially infectious is simply wrong an irresponsible as far as I'm concerned. I certainly wouldn't like to be a passenger on an airline that do that, even though I can see the difficulties that airlines face when there are a lot of potentially false claims of infectious diseases to get a free change of date.