There are reasons for him to take this offer, reasons that would make the offer better than a more lucrative one from a different team. I'm guessing, however, that if he wants to take a minimum deal, he'd take New England (and they'd be crazy not to offer the minimum for him).
For Miami?
First, he lives in the area. Second, he's injured, and he's NOT going to get the big money deal he really wants, so in all likelihood he may be fielding three year offers worth a total of like $7 or $8 million, MAYBE $10-12 million if they are backloaded deals with a lot of incentives and whatnot. That would be worst than a one year deal, even for the veteran's minimum. In that kind of deal, the team decides when he becomes a free agent again. With a one year deal, he decides. He gets to roll the dice, take the one year deal, try and stay healthy, show off his skills, and then receive the pay day at the end of the road (which would be significant if he stayed injury-free and showed that his injury didn't affect his skills). If he accepted a backloaded $12 million dollar three year deal, the team would only let him go when they feel he's washed up, and when they do, everyone will know he's washed up and won't give him big money. Why? Because he's just been dissed by his own team, cut, so everyone knows.
In Miami, under basically the same system as Belichick, Law would know he'd have a chance to prove to the league he still has it.
If I were Law, I'd start negotiating with teams and try to get one to offer him over $1 million on a one year deal. If nobody does, I'd try and retreat to the Patriots, or take the Phins' offer.