I know ARC's are not acceptable to be posted here on PBS.  

Today I received a book that has written in the top right corner of the cover,

"Uncorrected page proof: Not for Resale."

Does anyone think this just another way to say ARC??

I'm thinking I should mark it received with a problem and ask for my credit back.

Yes, that is how ARCs are marked by publishers.  

I found a letter inside the book from the publisher stating the book, is indeed, an ARC. I'll be asking for my credit back.

If the sender doesn't cooperate be sure to send a photo when you contact PBS about intervening. 

Why is it that we can not swap Arcs? Is there a place that does allow swapping or even giving/donating arc too? I am not looking to sell them or anything like that but I have quite a few and I am just trying to make room + share a good book. 

I would probably just donate an ARC if I came across one. This is from the help docs: 

An ARC  (Advance Reader Copy)  is an advance release of a book, usually sent to reviewers before the final copy of the book is published.

• Advance Reader Copies are also known as Review Copies, Early Copies, Advance Reader Editions, Galleys, or Uncorrected Proofs.
• They are softcover books and often carry the same ISBN as the hardcover first-edition that is released later.
• On the cover, they will be marked 'Advance Reader Copy' or 'Advance Reader Edition' or 'Uncorrected Proof' or 'Review Copy' and will usually also say 'Not for Sale'.

ARCs must NOT EVER be offered here, not in official nor unofficial swaps. They are absolutely prohibited, since

1. the ARC cannot be depended upon to contain the same story/text as the published book and

2. these items were given free to reviewers; they are not actual books.  The author and publisher did NOT get paid for the ARC and we do not support cheating authors/publishers. Posting an ARC is strictly prohibited, and ARCs may also NOT be swapped "unofficially". 

If you have an ARC (if you are a reviewer, for example) and are wondering what to do with it (since you can't swap it here):

• Some publishers are OK if you offer ARCs as a promotional giveaway on a blog or other book-promoting social media account -- since ARCs are intended to promote the book.
• Not all are Ok with this though. You can check with the individual publisher.
• Recycling the ARC is always a safe move.

If you mistakenly DO send an ARC, the requestor will probably contact you to ask for the credit back.

• You will need to do this. You can use the Give Refund button on the transaction in your Transaction Archive (after the requestor marks the book received with a problem/wrong book)
• You are asked to confirm, for each book you Post, that it is not an ARC. (So, if you Posted an ARC you broke the rules.)
• If you post an ARC after being told about the rules, you jeopardize your PaperBackSwap membership.
• If you receive an ARC, you should mark it received as a Wrong Book and send a message to the sender asking for your credit back.
  • You should NOT repost an ARC (or any problem book) if you receive one.
  • The receiver of an ARC should destroy/recycle the item.
  • Some publishers are OK if you offer ARCs as a giveaway on a blog or other book-promoting social media account -- since ARCs are intended to promote the book. Not all are Ok with this though. You can check with the individual publisher.
• The receiver of an ARC is not required to return the item; she or he may agree to do so if the sender sends postage for the item's return.  The receiver of an ARC should destroy/recycle the item. As with all problem books: the requestor receiving them is not obligated to spend postage to return them.

@Shannon M - You can look for a "Little Free Library" near you and donate them that way. https://littlefreelibrary.org/