You know, you hear this all the time, not just in this case, that the defense does not have to prove their client is innocent, its up to the prosecution to prove he's guilty (or She).
Say Amanda's lawer had one piece of evidence that proved Amanda was innocent, but didn't show it because of the unwritten law above, the outcome of the trial would be the same and an innocent person would be sitting in jail.
I don't know about you, but if I'm ever on trial for anything, and I'm paying a ton of money for my defence, they better try to prove me innocent regardless if I am or not.
I'm not a lawyer, but I think this is a misunderstanding of the concept. In a criminal trial the prosecution has to prove (beyond a reasonable doubt, in the U.S.) that the defendant committed the crime. He does so by presenting witnesses, security camera footage, evidence of motive and opportunity, fingerprints and other scientific material, etc. A defense lawyer doesn't have to prove that his client is innocent (and proving a negative is always difficult-to-impossible), but he does have to actively challenge and raise doubts about the prosecution's evidence. If the prosecution produces a witness that says Smith was at the scene of Jones' murder, his lawyer might produce witnesses that say Smith was somewhere else at the time, or work records that show he punched a time clock across town, or tape from a security camera that shows he was buying gas 100 miles away, or he might challenge the witness's credibility by asking whether the witness was wearing his glasses, what the lighting was like, was he sober that day, was he a convicted criminal, etc. If the prosecution claims Smith hated Jones, the defense might show that a lot of people hated Jones even more. If the prosecution says Smith was seen with a fat bankroll the day after the crime, the defense might show that he won a lottery. If the prosecution introduces scientific evidence, the defense will ask how it was collected, how it was stored, how it was tested, what qualifications the technicians had, what the margins of error were, etc.
The defense can't leave the prosecution's evidence unchallenged because that would mean all the jury would know about the case is what the prosecution says. Juries are usually given instructions to the effect that if the defense and the prosecution present equally likely explanations for a particular item of evidence, the jury must consider it in the light most favorable to the defense. But the defense has to offer its explanation. When a jury finds a defendant guilty beyond a reasonable doubt it means, in large part, that the defense did not discredit the prosecution's evidence to the jury's satisfaction. But that's not the same as failing to prove that he is innocent.
In the situation you cite, it's hard to believe that the defense would not present any and all evidence that would support his client, unless there was something about it that would cause other problems ("I couldn't have committed that murder because I was across town robbing the bank!"). Anything the defense presented would be subject to challenge by the prosecution, who might be able to raise doubts about what the defense claims as "proof" and might even be able to use it against the defendant. There is basically nothing that isn't subject to challenge on some ground or another. Maybe you could "prove" that you were on the other side of the world when the crime was committed, with airline and hotel records, passport stamps and more. Then maybe the prosecution would claim that you paid someone to masquerade as you to give you an alibi. (Pretty far-fetched, but you get my point.) Sometimes a defense lawyer will not even present his own witnesses and evidence if he feels that he has sufficiently discredited the prosecution's case during cross-examination, and he might fear that anything he could offer might distract the jury from what he hopes they will already see as weaknesses in the prosecution's case. But the defense can never just sit back and say, "I'm innocent, prove otherwise," because the prosecution usually will.