There were other concerns, too. He hadn't played football for very long, was a junior college transfer, and there were whispers - some perhaps planted by teams hoping to scare off competitors - that Pierre-Paul had character issues.
But to hear the Giants now, selecting the then-21-year-old was a no-brainer.
"Jason Pierre-Paul was a real easy pick for us," Giants general manager Jerry Reese said. "His skill set was so superior to most players that you see at his position or any position. We felt he had the highest ceiling of any player at any position in the draft. Why wouldn't you want to coach a guy like that?"
The NFL draft is littered with picks that were selected based solely on athletic prowess and flamed out when they reached the next level. In many cases, they didn't have the desire to put in the necessary work or couldn't mentally make the adjustment.
But Pierre-Paul, despite his indifferent demeanor, was hungry. Born to Haitian immigrants, his father blind from the day he arrived, Pierre-Paul often had to work through high school to keep his family afloat.
He entered the draft early for financial reasons. But now he is playing for history. Already he is being compared with some of the greatest defensive ends to play the game. His breakout sophomore season had much to do with the Giants' sneaking into the playoffs. And surely if the Giants upset the Patriots in Super Bowl XLVI, Pierre-Paul will play a large part.
"He's going to be one of the great ones," Giants defensive end Osi Umenyiora said.
Pierre-Paul said you could have seen it coming.
"If you look back and see the world that I went through and see every year that I was progressing and getting better and started to realize the game was even fun," Pierre-Paul said Wednesday, "you'll see I had a lot of potential of learning the game and being one of the greats."