Gifted kids shouldn't have to hide or be ashamed or scared of what they are. They will be if we are so we need to man up for their sake. The biggest battles I have had on recognition of giftedness and dispelling the myths of Giftedness have been with people with education degrees.
You wrote while I was writing.

Yes! One of the things that was emphasized (over and over and over) when I was studying gifted ed was just that: ironically, classroom teachers are the WORST (I guess this has been proven) at identifying gifted students. They tend to refer the "shiny apples" for testing...and are shocked when they don't test in the range.
Even more ironic: I feel like my son's teachers this year--who are all teaching only gifted students--did not seem to recognize some of his behaviors as being typical (if extreme--he is 2E) as potentially being related to giftedness. They are all green, though. If they last in the program, I suspect they will meet some more variations on the theme. The evil side of me hopes so.

Another common theme among educators (that will probably get a laugh, here)...a mantra, really: "it's not the gifted children who are the problem; it's the gifted parents." :P