Believe it or not, money is not the only motivator of people. Wanting to help someone you have a stronger relationship with (because one patient can communicate, the other cannot) could be incentive enough for some people. And doctors are, in the end, just people.
I am not suggesting that most doctors would do this, or even a sizable percentage, but it would be reassuring that measures would be in place to ensure what the GP is talking about cannot happen. I suspect everyone realises this, and there are actually systems in place to protect organ donors against harvesting whilst still alive.
Edit: this comment suggests the GP's fears are not so far fetched https://news.ycombinator.com/item?id=33300503 EEP!