You are overthinking it.
Your assumption is that because no one touched it, it couldn't break. That might be true of a block of wood or other, simple, chunk of matter; but electronics are active. The iPad is on. It may not be doing much, but it's is still doing stuff; electricity is flowing which means that stressed connections and circuits can fail.
The odds of it breaking by just sitting there are low, but not non-existant; espcially since it already had a broken screen. A broken screen means that the underlying electronics are no longer as protected as they could be.
It's also possible it broke the moment she set it down. Again, a broken screen means that the electronics under the screen are no longer as protected as they should be. It's also possible that your not-so-handy man left something a bit loose when allegidly repairing the iPad, and the small jar of setting it down finnished the job.
Or it may have finished breaking when you picked it up. Again, if the iPad has been abused (as this one obviously was), the cicuits may be on the verge of breaking at any time. Anything could finish the job.
You know, even cars have been known to not work the next morning, even though the seemed fine when you parked them last night. Especially a car that's been through a few rough experiences. iPads are considerably more complicated and delicate than a car.
If you don't find any of these ansers satisfactory, I have two alternate theories for you're consideration. Pick the one that makes you smile.
1) An Android using neighbor snuck into your house and used an AED (Automatic External Defibrillator) on your iPad. He will show up at your door next week with a sales brochure from Samsung. It's part of their newest ad campaign that pays commisions to everday Android users.
2) Apple's device oversite technician recieved a SOS from the iPad's distressed chips and send it an assisted suicide command. They also do this for obsolite devices. It is kinder, and cheaper, than piling them on an iceberg and setting them adrift.