It's just that no time can be 'wasted' (not an appropriate word perhaps, mcem), and the body needs to be taken straight away to the University. My friend is a retired minister who was a Chaplain at the Uni carried out this service sometimes.
There are occasions when the body cannot be used, at times such as when there has had to be a Post Mortem, for instance. I suppose that would mean that no organ could be donated in that case either.
Daughter not allowed to know new baby’s name until she visits him
Hair Straighener Brushes - are they any good?
What has survived in your garden with minimal or no watering?

I'm saying nothing. They're a funny lot. 