Not everyone who needs an organ transplant gets one. So could it be that recipients are privileged in some way that also prevents them getting dementia?
And each type of organ has different priority criteria. Kidneys for example you have a wait time and compatibility score. Liver is by MELD score and how healthy the person it (sick enough to need it but not too sick!)
Also a lot of transplant patients fall under Medicare and are not rich at all.