I'm surprised you didn't get a warning from the teacher -- she really should have e-mailed you several 'late assignments' ago about this, so that you could let your son know he needed to make a bit more effort to stay organized, or risk missing out on the class he loves.
That said, as far as her overall attitude (that the enrichment activity requires a certain level of organization), I'm afraid I side with the teacher, based on my experience as both a parent and a teacher. I have two reasons:
First, it doesn't seem unreasonable to me that organizational skills are required and/or emphasized in an enrichment class. When students at my school are invited to join an enrichment class (Latin, for example, in lieu of the vocabulary and grammar portions of Language Arts), they and their parents are told that it will require harder work of them than the regular class would; part of that higher level of difficulty is staying organized. I can tell you from experience that no matter how much HG-PG kids need or deserve to be in the class, they just aren't going to get much out of it if they don't have good study habits and organizational skills.
And if they've been getting that message consistently, from both teachers and parents, since the primary grades (that's a big 'if' with some kids!), they almost always do brilliantly in the enrichment class, because they have learned how to use their extraordinary abilities well.
Second, requiring a parent's signature on an assignment isn't meaningless. In my opinion it serves three purposes: it gets the child used to communicating with his or her parent about homework; it gets the parent to at least cast an eye over the homework; and it lets the teacher know both those useful habits are being developed.
