Correct. Another point is, as kids we are told that those people who are close to Allah, their bodies are protected in the graves and insects and other organisms are not allowed to consume them. Don't remember at the top of my head but have seen people quoting some hadith too. Those people also give example of Ashab-e-Kahaf, who, together with their dog, were made to sleep for a very long period of time and Allah protected their bodies during all this time. Yes, we try not to bring religion in but these teachings are part and parcel of our upbringing and come into play and or affect our decisions pertaining to issues such as organ donation.