I always thought the genius label was pretty silly. The Jets have never done anything to reinvent the wheel with the cap. Other teams in the league are far more creative with the cap such as the 49ers. Other teams are more proactive with their contracts like the Patriots and Eagles.
I think the one thing that the Jets have done is construct contracts with trades in mind and contracts that highly encourage offseason participation. While trades in the league are rare the Jets are very aggressive with them and they have structured deals to more or less make anyone on the roster available. That fits in with the team philosophy even if it seems a bit unconventional.
Its really been the last two seasons where it has gotten messy. It was really 2011. The Jets more or less removed their fiscal constraints and went a bit overboard in free agency in a hope to win now. I think it goes back to Rex honestly. He wields too much power and it blinds the team to reality. Even in 2010 the Jets were prepared to stand firm on Revis but Rex forced it through. Since then he was ineffective for half a year because of a hamstring and missed just about all of 2012.
I think, if the system stays status quo, the jets need someone to bridge real performance evaluations using historical standards as a basis for the riskiness of a contract and tie it into the contract makeup. Too much is just done by "gut reactions" from the coach.