At age 5 you could safely wish for "I wish for you to do what I should wish for" and at worst you'd be a little disappointed if what she came up with wasn't as fun as you'd have liked.
I would have gotten the wrong flavor of ice cream. It was strictly better to specify the flavor of ice cream I preferred. Therefore, the statement about the 3 types of genies is simply false. It might be approximately true in some sense, but even if it is, the article never gives any arguments in favor of that thesis, it simply gives one example.
Wait, to be clear, you're calling getting the wrong flavor of icecream a "safety" issue?
Do you have any examples that actually fall outside the 3 types? Your mother is likely not powerful and nor is she a superintelligence. So far the only example you've given has fallen squarely in the third category but even if scaled up would probably fit quite well in the first.
I'd also note that the claim you're taking issue with is a metaphor for explaining things, he's not claiming that magical genies actually exist of any category.
https://www.reddit.com/r/science/comments/3nyn5i/science_ama_series_stephen_hawking_ama_answers/
the vast majority of the discussion is about AI risk.