They are wrong to think that (I’ve studied medical errors and their coverups behind the scenes for years, never once seen evidence of that, plus transplants of vitals are so high risk that saving the current patient if you can would pretty much always optimize your lifesaving rate however you keep score). But even if that were a reasonable thing to worry about, that’s all the more reason to remove it as an issue by not asking the dead what they want done with their organs
Doesn’t complicate the situation in any way. Less important than the rights of the living to be alive (and anyway; the rights of the fam aren’t absolute even under the law as it is, it’s a common misconception that they just own the body & can do whatever with it). And there’s 0 risk of that since anyone who needs a vital organ transplanted isn’t in a condition to kill anyone in the meantime (plus you’d have no way to control who gets your victim’s organs annyway)