So, I mailed out a book I had posted, and it's way over the time it should have taken to get there 1st class. I PM'd the member, and they said they had the book mailed to someone else. Is this allowed within PBS rules?

Yes it is allowable.  When you order a book you can have it sent to yourself, or fill out the form for another address.

I know of at least one swap where members order books off of the site for other members.

I've done it, but the person who's getting it needs to be aware that they need to inform the person who had it sent to them that they need to let them know so the person who had it sent can mark it received.  Hope that makes sense.  Pat

Yes, when you order a book you are given the option to send it to a friend. They are supposed to find out from this person when the book arrives and mark it recieved. How long has it been? I've had books sent first class take quite awhile to get to their destination. If anything I would just reply and ask them to please mark the book as recieved when they hear that their friend has recieved it so that you can get credit. If it's only been a week (or less) it could very well have not reached its destination, and I would just give it some more time.

I use this option a lot.  I order books sent to my niece, a first grade teacher.  (Her classroom wears out a lot of early readers.)  And I know she does not have internet or a phone at home.  So I'll mark them as received even if I have not heard from her. 

Since you cannot mark a book as RWAP when you sent it to another address, waiting does not make much sense.  But it is up to the person in the middle to mark it received.  I'm wondering if the person who did the order does not know this.