Some theories of how the wards could (a) not detect Hermione was wounded and (b) claim that the Defense Professor killed Hermione.

Wounding wards:

1. Wards were tampered with
2. Hermione's battle was fake. Hermione was not wounded during battle. When Hermione appeared to die, the Defense Professor killed another witch.
3. Dumbledore says "If Voldemort wishes us to distrust a truth told by the wards, then Voldemort has not fully mastered the wards. And in that case the wards had to believe that some Professor's hand was at work, or they would have cried out at Miss Granger's injury, and not only upon her death.". Perhaps this means that any teacher can circumvent this ward

Defense Professor killer ward:

1. Wards were tampered with
2. See wounding ward theory 2.
3. The Mountain Troll was the killer. To identify the Defense Professor to the wards, Dumbledore drew a circle and said that that "he who stood within was the Defense Professor". Quirrell arranged for the Mountain Troll to be in the circle. This explanation might require polyjuice, transfiguration of live organisms, or Quirrell to be female.
4. A previous Defense Professor, thought to be dead, was the killer.
5. Mountain Trolls are considered weapons, as Dumbledore said. "it was no stray creature, but a weapon pure and aimed." The wards blamed the aimer of the Troll, not the Troll itself.
6. The Troll was a witch. The troll's death triggered the wards.

EDIT Added Defense Professor killer explanation 5 and 6.