Having been in several countries with endemic YF and even more that require a valid proof of vaccination, my experience is that it's not the airlines checking the certificates but immigration or public health officers (if checked at all). Mind you, I have never been to the Bahamas, though, so no idea how they handle the requirements there. Still, I was never, ever asked by an airline to show the vaccination booklet and given OLCI, etc. I doubt that anybody would ask for it at the gate at the time of boarding.

At any rate, the chances of getting YF at the Panama City airport are close to zero, the chances of dealing with a narrow-minded inspector in Nassau are higher, I would suggest that your friends get vaccinated...