The Church and Organ Donation

I was reminded today, when people at rehearsal (I'm so tired, I'm so tired, I'm so tired....) spoke about surgery:
As I was driving to church for choir last night, (or rather, to the rectory and the Blessed Copy Machine, my best friend and patron saint, although unlike my predecessor, I don't think I am ever spoken of as having "toner in my veins,") I heard maybe 20 seconds on Relevant Radio, Drew Mariani, I think the host of the show is?
And from a snippet of conversation, obviously the tail end of the discussion, I received the impression that someone had espoused, or at least failed to debunk, the notion that live donor organ donation is somehow not in keeping with Catholic teaching, if "beauty" is affected.
Tell me I heard wrong, and no one thinks anything so absurd, and dare I say, evil?
Anyone (of my 2.7 readers,) ever heard such a thing?