I corrected myself straight after I first posted. You must have taken over 5 minutes to post. I'm amazed you managed to see what I had written incorrectly. I realised immediately that I was thinking of one of the other sorts.
You can definitely sort a doubly-linked list by swapping values. A number of coders who are used to array sorting try this as their first attempt at linked-list sorting. I certainly agree, it's a very bad idea and you've pointed out one reason why, but some people do it. The other reason is that you are stuck with algorithms that are O(n*n) because you have neither random access, nor tha ability to 'insert' items as you would with a list. I never intended to imply that swapping values would be the normal way of doing it.
Edited for spelling this time.