Well you just answered your own question. If the Giants wanted to make sure no one else was able to claim him, the price should have been higher than switching late round picks two years from now.
Another possibility is cutting a vested veteran and keeping Basham on the active roster then re-signing the veteran later and moving Basham to the practice squad. If somebody wanted to claim him after that, they'd have to put him on their active roster which might deter some suitors.