Pieces of the puzzle is an idiom. It means kind of like information about something. Think of trying to figure out what the first quarter figures will be as like a puzzle. If you have all the information you need then that is like having all the pieces to a puzzle. If you have some information missing then that is like missing some pieces of the puzzle. For your example, the expectations about first quarter figures would change as people learned more information about the business, so you could say that the expectations fluctuated as pieces of the puzzle emerged. The sentences "Me and my friend had both received a letter" and "My friend had received a letter, as had I" both mean exactly the same. "I had received a letter, as had my friend" also means the same. It doesn't really matter which one you use, they are all grammatically correct. So your example could be written as "The FBI and John McCain had also received copies of the allegation" or "John McCain had received copies of the allegations, as had the FBI" without changing the meaning.

Pieces of the puzzle is an expression. It relates to how a mystery or uncertain situation becomes clearer as more information is known to how the completed image for a puzzle becomes more obvious as you place pieces together. In this case, 'pieces of the puzzle' refers to information that made the people's expectations for quarter figures change. Let me know if that makes sense. I can provide examples if you like :)