As it turns out, they are not allowed to, other than the mini. offer they did give.
So, nobody to blame for this mess. :-(
Why didn't the Knicks just give Lin a fair offer to begin with?
They couldn't. As a player with Early Bird rights, his current team was only allowed to offer a first year at the league average—around $5 million—and raises of just 7.5 percent each year after that. The Rockets could give him whatever they wanted, and the Knicks could match that, but New York didn't have any choice but to wait for him to sign an offer sheet.