You're both right. It both sounds odd to me and is perfectly correct. There's a rather plausible explanation of that phenomenon for this particular word here. I don't agree with the analogies you provide to "cutted" and "hitted", since you're literally making up non-words there, but the analogy to "put" on that page resonates pretty strongly with me since "input" obviously descends from "put".
Edit: Also, "it sounds odd and is perfectly correct" doesn't mean you should leave it that way. It means you should change it, because when it comes to written text in this genre, being right isn't nearly as important as sounding right.