This one is actually the least crazy of the lot, I think - the super-Patronus works on the principle of love for all human life. Someone who casts it ought to be damn near incapable of murder, and if the principle could be explained to the Wizengamot without ruining everything, the fact that Hermione managed it would actually constitute exculpatory evidence.

Love of all human life does not translate into an inability to do math or unwillingness to murder.

As well, it's not clear that guilty Hermione feels good enough about herself or all human life that she would be able to cast it.