I had a book on my wishlist and received a notification that my book was available to request.  After requesting the book, the sender PM'd me and told me that someone else had requested the book before I did. 

I thought that I had the exclusive right to accept or decline the book for 48 hours before it gets offered to anyone else.  How was it that this book was "snagged" out from under me?

It shouldn't be possible.  The system is set up to prevent that from happening.

Probably the member has an account on other book swapping sites and the book was requested at another site.  It happens from time to time, it's the danger of posting the same books on other sites.

ETA:  Check out this post - is this the person you requested the book from?  http://www.paperbackswap.com/forum/topic.php?t=151814

Occassionally there is a glitch where it posts a book twice.  So it's possible that this happened to that person. It happened to me when I first joined. I posted a WL book and it offered it to 2 people at the same time.  There is no way to delete it until someone accepts the offer. 

It's also possible that they were trying to post the WL book directly to someone else and it put it to FIFO instead. 

Or they used it for a game and posted the book to Mail to a Friend not realizing that you can't do that with WL books.