Graham and his agent were arguing that he lines up as a wide receiver so often that he should be classified as one. The Saints offense uses Graham in a way that is unique compared to most other tight ends, and his numbers are far more comparable to that of a WR than an average TE, or even compared to most other elite tight ends.
The NFL arbitrator eventually came to the decision that Graham is indeed a tight end, meaning he'll get the lower tag number and any contract extension negotiations after that will start with the Saints having a clear advantage.
This is a huge ruling for the league, and could have a big impact on how players are willing to negotiate in the future. Graham knows that his value isn't even remotely comparable to other tight ends in the league, and he could hold out for more money knowing that the Saints will eventually have no choice but to give him his money.
One of the main factors appeared to be the way defenses played against Graham. Since he was often defended by linebackers and strong safeties, that categorizes him as more of a tight end than wide receiver.
According to the arbitrator Stephen Burbank:
Burbank obviously didn't note that when Graham was covered by a player who typically covered other tight ends, he dominated them. He didn't note that the only time Graham was truly shut down was when he was treated like a wide receiver, when teams like the New England Patriots put elite cornerbacks on him, like Aqib Talib.
Realistically, Graham's skill set and performance dictates that he deserves to be paid like a wide receiver. Not just any wide receiver, one of the better WRs in the league.
He's not a typical tight end, and he's better than 'just' an elite tight end. And he deserves to be paid as such.