What does "死ぬ事は不正直である。" mean? I would translate it to "Death is dishonest." and Google translate seems to concur. However, Jisho.org where I got this example from, says it means "Death is preferable to dishonor."

I think Jisho.org is incorrect on that one. would not mean "dishonor".
I'd translate rather as `Dying is dishonest`, or `To die is to be dishonest`, but it'd be a weird sentence.