I don't mean to nitpick, and the rest of your post is spot-on, but technically, the defense team doesn't even have to go that far. The prosecution has to prove every element for guilt to be established; if they fail to do that, then not-guilty is required. So the defense team could, legally anyway, say absolutely nothing.
I saw this actually explained to a jury pool by a defense attorney during voir dire (that's the process where a jury is selected) when explaining the State's obligation to prove every element. They also said, of course, that a defense attorney doing nothing and presenting no counter-evidence is strategic suicide.
I just wanted to bring that up because your comment brought the moment to mind. Food for thought and all.
Your point is well-taken, and as I hope everyone knows, I am not a lawyer.
In the end, it comes down to the jury, no matter if the defense presents a theory of the crime, offers mitigating circumstances, casts doubt on the prosecution's evidence and testimony or whatever. The jury either believes that the accused has been proven to be guilty beyond a reasonable doubt or they do not. The usual instructions to the jury from the judge generally include information about what 'reasonable doubt' is.
What I meant by my comment is that the defense's job is to establish that reasonable doubt in the jury's mind. They can do it in a variety of ways, including facts and testimony that tend to establish actual innocence, as well as by contradicting prosecution evidence and witnesses and so on. Theoretically, if they felt their case was so solid it required no defense, they could certainly sit mute; however, I would suspect that if they had a case that solid for actual innocence, they'd ask for a dismissal with prejudice and get it.