It turns out it was a little more than awkward. It was against league rules. Mike Freeman of CBSSports.com first reported that Irsay will not be allowed to use his plane to help Luck out.
Luck isn't allowed to practice with the team until Stanford graduates, but this news may have more to do with the salary cap. If owners were allowed to give a player unlimited travel on his private plane, it could be viewed as a bonus. That would be a way of skirting the salary cap.
It should be no problem for Luck, who hopes to go to Miami to work with Reggie Wayne. The rookie salary cap may have lowered his first contract, but he should still have plenty of money to buy an airplane ticket. He could probably even splurge for that row with the extra leg room.