Fury
He wanted the kid. No matter what was going on with his summers and the explosions or anything else. The kid would be a valuable asset. They needed someone young to train in the event they ever needed to replace an Avenger, someone young enough to be impressionable but old enough that they weren't going to be completely idiotic. Or anymore so than the current Avengers were bound behave anyways. Perseus Jackson fit the bill perfectly.
He'd evaded SHIELD agents for weeks, kept them off his tail for years and managed to escape the Avengers once and noticed enough of them to almost escape a second time. He was the right age to begin grooming for the next generation of the Avengers Initiative. Fury leaned back, appearing to be completely relaxed. Really he was calculating every factor, every variable he needed to control in order to get the result he wanted.
"Who are you?" The kid asked bored, as though the question was a courtesy he was extending. Fury raised his eyebrow.
"Director Fury."
"Why am I here Director Fury? Fourth of July here said that he didn't want to bring me in but the boss man was making him. I'm assuming you're in charge of this joint?" The kid had a mouth, and some serious balls; Fury would give him that.
"I'd like you to train with the Avengers. Be a...ah, trainee of sorts."