I would hope that everyone would be OK with providing their fellow pilot, who was "sick", due to a fall (unless it's caused by too much adult beverage
or getting beaten up, a ride home. After all it's the humane thing to do, while at the same time I don't think that you'd have much chance of catching what caused them to be taken off their trip in the first place. As opposed to giving a ride to someone who is obviously "sick" with: flu-like symptoms; is running a fever; is coughing and sneezing all over the place; or is in obviously poor health. Giving that person a ride jeopardizes everyone else on the flight. Personally I would applaud managements' decision to allow someone in the former category, to jumpseat back to base or home.