I assume you mean the jury, and yeah, they absolutely can disregard testimony that they do not find credible.
Here's two non-Florida sources:
http://www.jud.ct.gov/ji/criminal/part2/2.4-2.htm
http://www.nycourts.gov/judges/cji/1-General/CJI2d.Credibility.pdf
I didn't waste my time finding a Florida-specific source, because this is a really basic thing that is true everywhere. And really you're arguing with me and agreeing with me at the same time. The jury's choice to not believe Dunn, if that is their choice, would be based on the rest of the evidence that has been or will be presented at the trial. E.g. if they decide that the victims couldn't have disposed of the imaginary shotgun, and they decide that Jordan Davis probably didn't threaten Dunn or get out of the SUV, because the argument was witnessed by other people who didn't see Davis get out and didn't hear him threaten Dunn (but did hear Dunn say "you can't talk to me like that").
The jury won't just arbitrarily decide to ignore Dunn's testimony, but it is very possible that they won't believe he is telling the truth. And his testimony is the only evidence of self-defense, so if they don't believe it Dunn will not have created reasonable doubt as to whether he acted in self-defense.
This would be much easier if you would refrain from lying.
http://www.ohioverticals.com/blogs/...burden-of-proof-on-the-issue-of-self-defense/
Like I said, if Dunn can't provide evidence (e.g.
credible testimony) that he acted in self-defense, then the state doesn't have anything with regard to self-defense. Dunn only needs to create reasonable doubt in the mind of the jury, which is a low standard to meet, but his claim of self-defense is not accepted at face value like you are saying.