First of all, it's likely that Martin never would have even tried FA if the Pats had not low balled him in the first place. Having said this, yes I understand that after a year, Martin and Parker could void the deal but that doesn't change the fact that if the Pats had wanted to kill this deal, they simply needed to counter by offering more money, rather then matching. The Pats didn't do that.
Jets offered a 5 year, 28 mil deal with a club option year for and additional 8 mil, bringing the entire deal to 36 mil. The "poison pill" was the void of the clubs ability to use the Franchise Tag. In addition to this, the Jets offered a trade to the Pats for their 1999 1st, 1998 2nd, and a 3rd and 4th in 1997. This was what really forced the Pats hand. They weren't afraid that Martin would void the contract. They were afraid that they would lose out on that trade value. All the Pats had to do was offer a better deal to Martin and the whole poison pill deal was off the table but they didn't do that . They didn't want to spend the money and they wanted the draft picks.
That's how that deal happened. So as I said earlier, the Pats could have kept him if they wanted to but they don't let any player, even one as good as Martin, effect their plan.