So do you still believe that to be found not-guilty you have to prove that you're innocent?
FWIW there are circumstances where this may be the case. These are usually referred to as "affirmative defenses". I had a quick look at the Texas Penal Code and it provides for a couple of examples, including insanity and duress (see Title 2 Ch. 8). The Texas Penal Code provides at s. 2.04 as follows:
Quote
Sec. 2.04. AFFIRMATIVE DEFENSE. (a) An affirmative defense in this code is so labeled by the phrase: "It is an affirmative defense to prosecution . . . ." (b) The prosecuting attorney is not required to negate the existence of an affirmative defense in the accusation charging commission of the offense. (c) The issue of the existence of an affirmative defense is not submitted to the jury unless evidence is admitted supporting the defense. (d) If the issue of the existence of an affirmative defense is submitted to the jury, the court shall charge that the defendant must prove the affirmative defense by a preponderance of evidence.
(emphasis added)
It doesn't appear that self defense is an affirmative defense in Texas though. There may be jurisdictions where it is, but there again I'm not licensed to practise law in any of the states of the US.
