Idiotically intelligent means that in dumb situations like setting a can of soup on fire with pepper spray you know what to do and you're smart in that situation.
We can also mean two smart to be done but too dumb to be smart
Do you know how that squirrel jumped through Emma's window and snatched her pizza she was so idiotically intelligent by smacking the squirrel with a book
someone SO FUCKING STUPID you have to say the same word 3 times and each with different endings
Kid 1: "Santa is real."
Adult 1: "No you idiotically idiotic idiot, he's not real. I was told that if I ate this pill my dick would grow 3 inches, and I fucking got erectile dysfunction. Don't believe everything you're told, cunt."