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."
The Eagles instead chose to draft defensive end Brandon Graham. Eagles general manager Howie Roseman equated the choice between the two as hitting a double as opposed to swinging for the fences Dave Kingman-style.
The Giants, though, hit one out of the park.
"All players are risks when you draft them," Reese said. "It's not science. Sometimes, they can play at a high level in college for four years, and it can look like a duck, quack like a duck, walk like a duck. Then you get them out on Sunday in the National Football League, and it's not a duck, even though it looked just like a duck when you scouted it."
Because the Giants had so much depth Pierre-Paul was eased into the defensive-end rotation as a rookie. He recorded only 41/2 sacks last season, but the Giants say they knew he was special from the start.
"He's impressed us since the day he walked out there on the field for the first time," Giants linebacker Mathias Kiwanuka said. "You see him, and he's a physically imposing guy. This year he made a number of plays where you watch it in film and you say, 'How did a young guy understand what they were going to do on that play?' "
Fewell knew something had clicked during the long NFL lockout when he saw Pierre-Paul make a play during a preseason game against the Panthers.
"He made a Reggie White move against one of their really good tackles and I said, 'Wow, I haven't seen that out of JPP,' " Fewell said.
Pierre-Paul's teammates used to tease him about his lack of pass-rushing moves. He really didn't need them because of his strength and size. But now that he has added swim and spin moves he's been almost unstoppable.
"Probably about five times a game he has plays like that," Patriots coach Bill Belichick said. "He comes out of nowhere and makes a tackle or jumps 10 feet in the air and bats down a ball or makes an athletic move at the line of scrimmage while keeping his balance. He's a rare athlete."
Pierre-Paul's 161/2 sacks this season are the third most, behind White and Richard Dent, for an end in his second year.
Pierre-Paul said he gets much of his drive from watching how his father - who he said lost his sight for reasons unknown - lives his life.
"Most people, when something like that happens, they just think their life is over," Pierre-Paul said. "But that's not true. My dad can still do things like a normal person. He still cooks, watches my sister's and brother's baby when my mom's not home. He does things like a regular person."
Pierre-Paul didn't play football until he was a junior and suffered a leg injury playing basketball. He almost quit football, though, when he took a job at Boston Market to help supplement the family income.
"I told my coach I can't play football because I have to make money to help my mom," Pierre-Paul said. "So I went in to talk to the manager, and he asked if I was playing football, and I said, 'Yeah.' And he was like, 'You know what, I'll adjust your schedule for you when you get out of practice.' "
The rest, as they say, is history. Pierre-Paul's family will be here for Sunday's game. He still has a ways to go, however, before his name is etched alongside the greatest in the history of the game.
"They don't have a bust of him in Canton waiting for him," Reese said. "He's still got a lot to learn. But he has come a long way in a short time, and we think he's barely scratched the surface at this point."
Contact staff writer Jeff McLane at 215-854-4745, firstname.lastname@example.org or @Jeff_McLane on Twitter.