This strikes me as nonsense, but I'm not picking on you. A lot of people around here (on .NET) have been saying this since the trade, and the logical fallacy you're all committing is extremely common among us human beings.
Trading for Williams gave the Seahawks no advantage for re-signing him. If he wants to be a free agent, he'll be a free agent. The fact that the Seahawks gave up a second-round pick to get him doesn't change that. More importantly, it should also change nothing in the Seahawks' calculations of the contract terms they're willing to give Williams. What they should be willing to offer him
should be exactly the same as what they'd be willing to offer him if he had not been traded to the Seahawks and instead played out his contract with the Giants or some other team.
The second-round pick the Seahawks traded for Williams is what's known in economics as a
sunk cost. I hope the Seahawks front office is smart enough not to fall into the trap of the sunk-cost fallacy.
From the article on sunk costs I linked above and put in the color closest to "action green" I saw, there's a pretty good description of the sunk-cost fallacy: