If you analyze the specific details of the trade, it's really apparent that it was primarily just a salary dumping move by Miami. Crawford and Brooks went to Golden State for the low, low price of Toney Douglas... who they sent to Miami, not Boston. Essentially, Golden State took Crawford from Boston for free and got Miami to foot the bill. Miami was willing to foot the bill because it benefitted them financially.
Of course Golden State viewed Crawford as an upgrade over Douglas, but it's really clear that Boston got those draft picks purely because they were taking on Anthony's contract. Golden State didn't send a thing to Boston for Crawford, so yes, those three draft picks clearly were compensation for Anthony's contract.