The Knicks said from the start that they would let the market dicate Lin's value.
The only offer sheet presented was the 3 year deal with the poison pill. The initial reports was that Houston was going to offer Lin a 4 year $28.8 million deal. $19.5 mil was to be guaranteed over 3 years with a team option in the 4th for the remainder. This offer was never put in writing but this is the offer the Knicks were expecting and were seriously thinking about matching.
Lin then went to Las Vegas to meet with the Rockets to renogotiate the deal and to sign off. The Knicks didn't know that Lin was doing this until it was done. In fact the Knicks were in Vegas for summer league at the time. The only offer sheet presented was the 3 year deal Lin signed with the poison pill in the 3rd year. 3 year a little over $25 million with $14.8 due to Lin in year 3. http://www.nypost.com/p/sports/knicks/lin_match_stick_SaOeWm9GmE9b6FjL2sxQLO
Had Lin not renogiated the deal with Houston, the Knicks would have probably matched the offer. However, when the actual offer sheet came up Dolan got mad that Lin schooled him and felt that Lin was not being loyal. Personal grudge? Absolutely. Dolan also had his "basketball people" telling him that Felton was just as good if not better than Lin.
"From a "person who has had business dealings with Dolan": "I don't think this is about the money as much as it is Jim feeling that a player isn't showing the Knicks the same loyalty they showed Lin. Don't forget, the Knicks gave Jeremy Lin a chance. Then Jim has his basketball people telling him that Felton is every bit as good if not better than Lin so it makes the decision easier for him to make. Jim can be vindictive but sometimes that's a good thing in the NBA." http://www.grantland.com/story/_/id/8174968/jeremy-lin-leaving-new-york-knicks-james-dolan-blundered-again
Lin did what every other player in the NBA does come contract time....go out and get the most money you can for as long as you can. Sure, Dolan could have just matched the offer and brought Lin back but he wasn't going to put his personal feelings aside. Instead he gets the sign and trade done with Portland to bring back a "loyal" player who never wanted to leave and wanted nothing more than to get back to the Knicks.
It could have been handled differently by both sides but Lin is not blameless in this either. If Lin really wanted to stay with the Knicks it would have happened. Personally, for this team right now I think Felton is a better fit.