It's a little harder than that; transplant centers are all tied into one central agency that controls the data of transplants. If joe bad liver is listed at transplant center x, all transplant centers will know and see his name on the transplant lists. I've been looking into this and a joogle search claims about 40% of transplant centers require the vax, but there's an awful lot of posts about people being turned down for listing as recently as this year. Since JD Vance's relative has been denied, some govt wonk is pushing a bill to ban denying transplants for covid vax.