Pulling out my dictionary (...again, sigh):

1.fully aware and attentive; ,wide-awake; keen: an alert mind

Can any of us think of antonyms for wide-awake?

So if the gifted literature is clear that gifted babies are often more alert, then what are more typical babies doing? Maybe looking sleepy? Maybe with that glazed eye look we all get when we are sleepy?

I suppose if you are looking to be offended, you will be, no matter what I say.
No matter what the dictionary says!

Be offended! Yippee for you! What a wonderful attitude to have in life.
Good luck with that.