Nero was far too skilled with the abilities of the Devil Bringer in his first fights of the game for it to have just then developed. Also, he was not at all surprised when it exploded out of the cast upon touching Rebellion...another of Sparda's weapons, mind you. The fact he was well aware of its default powers means he'd been hiding it and what it could do for some time. If it was some "infection", I'd think he would have been trying to get rid of it before hand, and the Order would know about it in some degree.
BTW, via concept art, we know that the Bringer is in fact his ENTIRE right arm, not just up to the elbow like some fanart was assuming. Also, the attack in the forest was actually mere days before the festival, which means Nero has been hiding the Bringer for some time. He would not still be in a cast if the attack had been months before hand, since he didn't take that serious an injury from the manual's detailing. His upper arm was wounded, not his whole arm. Credo also wasn't very surprised by the revelation of Nero's power, which means he knew all along. While Nero might not have been born with his arm as it is in the game...it's something that would have developed it seems, regardless of any external demonic influence.
Ergo, this brings the conclusion...Nero's power is definitely connected to Sparda, since the weapons that triggered it to reveal more powers were the blade that Sparda created, then passed to his sons. First it was Rebellion impacting on the Bringer that awoke the full form(and didn't leave even a cut, mind you), and then Nero's anger and desire to fight back restored Yamato.
And to anyone that still says it gains power by absorbing pieces of Nero Angelo...sorry, not the case, the only Nero Angelo presence is actually the Order's own artifically "angel-formed" soldiers.