I know, what are the odds, right?

Removing someone for a safety of flight issue is always ok. Someone who could pose a danger to themselves or others during an evacuation is one litmus test to consider.

The question might be asked "you're not a doctor so how can say I'm sick?" to which the reply might be "I'm not a doctor which is why I cannot say you're not sick" if someone has outward signs of being sick.

Couple this with going through customs in which the captain certifies no known communicable illnesses and it may be prudent to have them checked out.

Recently on my airline a woman was in the lav throwing up repeatedly during boarding. FA's brought it to our attention, and us to the gate.

Options were, call airport paramedics, call medlink for advice whether to keep her on or not, or voluntarily get off the plane.

Much to our relief, she and a family member did just that, with no fuss. Phwew!

Throwing up the same day as a flight and admitting as much will require many airlines to remove you as policy.

While the family was put under additional strain the daughter must have been very ill to have a FA notice. Curious what the sick daughter thought of flying that day. As always there are two sides to every story.

True, I am hearing this story second hand from the parents.... As a pilot my first reaction was to recognize that it was a conservative decision with safety in mind. I think mom and daughter shared too much info with the FA not knowing that the end result would be removal from the aircraft....

Having children myself, I also recognize that their health often changes quickly....
Removing passengers that appear unhealthy raises some issues... it's not like we are taking them on a thrill ride, we are putting them in a climate controlled environment with access to water and restroom facilities. At a minimum I believe that a crew member or agent that makes the decision should be able to be confident that they believe that allowing the person to travel would result in harm to the individual or others and that a diversion of the aircraft could be likely.....
Thankfully, as pilots, we are probably out of the loop when these types of issues occurr since the ground staff is still involved...

I would be curious to know which airlines have the specific policy you mention....

Why was the little girl (bless her heart) throwing up? Norovirus, perhaps? Not saying that is the case, but we all know the symptoms. Unless they were certain it was not, the parents made a deliberate choice to expose everyone on that flight and contaminate the airplane.

Last year, some of my extended family members came to a family gathering a couple of days after the "stomach flu" had gone through their household. We all got it.

Sharing is not always caring.

Also, many people buy the lowest fares with no allowances for changes/cancelling so going to the airport even if probably sick is still better to them then losing all their money.

At least if they are removed they get rebooked by the airline.