they didn't offer any cause they were just planning to match any offer that's in the table for Lin and they didn't expect him to sign any offer sheet.
They felt betrayed cause the 1st offer sheet Houston planned to sign Lin to a four-year, $28.8 million sheet — really three years and $19.5 million, since the Rockets would hold a team option for the fourth year — with the so-called "poison pill" coming in the third year, when the 23-year-old point guard would be due a $9.3 million payout but Lin went back to Houston and rework the deal w/c the is new offer sheet he signed the $25.1 million 3yrs with the "poison pill" in the 3rd year with $14.9 mill.
He was milking it and Good for him but i understand why the Knickerbuckers felt betrayed cause they were the only team who gave this kid a shot to play in the biggest stage in basketball when everybody was counting him out. If it wasn't for the Knicks there won't be any "Linsanity"