No they couldn't. If there's a kid running around who's hair regrows to the previous length the night after it's cut, had windows disappear before his eyes, and all the various other stuff that happened to Harry in the books before he found out he was a wizard then his parents have much bigger fish to fry. He didn't have your normal run of the mill wierdness hapen to him, no big coincidences or anything petty like that, he had high profile unexplainable occurances happen fairly regularly.
No this isn't new age gnosticism, it's a STORY about an IMAGINARY world where wizards really exist and it's purely a genetic trait. The only thing it's an invitation to is buying the merchandising, like any other mass market product it's all about the benjamins.