"I never argue with people who say baseball is boring, because baseball is boring. And then, suddenly, it isn't. And that's what makes it great." - Joe Posnanski
Hamilton's camp had not actually rejected their 4-year offer. The Angels stepped in and offered 5 years and they never got a chance to match or go beyond it.
Offering 5 years when the 4-year deal was being considered is bad negotiating. You would be throwing money away doing that. There was no reason to offer more because the previous deal had not even been rejected. Like I said, I wish I had you to negotiated with.
"Oh hey, I know I just offered you 4 year and you're considering it, but how about I give you 5 years instead?!"
"No matter how good you are, you're going to lose one-third of your games. No matter how bad you are you're going to win one-third of your games. It's the other third that makes the difference." ~Tommy Lasorda
Sure, Hamilton's camp didn't let the Rangers match and that's too bad for TEX if they really, really wanted to re-sign him. It may have been that Hamilton was just ready to move on because of how the season ended. There was a lot of disappointment with him from the fans and people in the front office said they didn't want him back for free. Nolan Ryan and Daniels may not have been of that mind but maybe Hamilton had had enough and they couldn't have got him even with a 5th year. And maybe the Angels told him that their offer was good right then and there. If he walked, they would have taken years or money off the deal.
But TEX may have lost Hamilton but they can save face with the fans who still wanted him to come back since they offered the 4 year deal and he didn't give them an opportunity to equal or better the offer. But if they really, really wanted him to come back, even if they offered him a 4 year deal, why not come back and offer him a 5th year if you haven't heard back from them in a few days? Maybe that's bad negotiation to you but if it got them what they wanted, who cares?