Because NICS checks aren't run against range rentals. A form 4473 would have caught this, so she wouldn't have been able to buy a gun (due to the fact that she had previously been in a mental hospital), but renting a gun at a shooting range doesn't require a 4473. I wouldn't be surprised if this is the first such incident ever to occur, so it's not surprising that nobody has ever tried to get NICS/4473 requirements attached to range rentals.
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