As a parent, you are perfectly within your rights to ask to see your DD's records, and to make copies of anything you find therein. You're also perfectly within your rights to request a meeting with whomever you feel is the right resource to sit down and discuss exactly how they arrived at the decision to approve gifted services for your DD.
As for the perceived executive function thing, it seems like they're looking for a particular type of initiative that they're actively discouraging at the same time. Think of it in culinary terms: they're telling her that if she really needs cake, she'll want to eat more liver. That's not an executive function problem... that's a revulsion problem. A kid who eagerly does work that's significantly below your DD's level is, by definition, significantly below her level. So they're not looking for gifted, they're looking for brighter than average. I would point this out. I would ask the teacher how much she'd enjoy printing her ABCs.
As for the minor errors... that doesn't sound like ADHD, that sounds like being a top-down thinker, who sees the forest and doesn't pay much attention to the trees. The downside of this kind of thinker is they're prone to careless mistakes. The upside is that this kind of thinker easily demonstrates mastery once they've learned the high-level concept, immediately integrates new concepts with those previously learned, makes new associations, and can even spontaneously arrive at the next concept without being taught. So, you teach the child to be a little more careful, and hang on for the ride.
