Let's just be perfectly clear here (post I am replying to was deleted):
Jesse Ventura did not go through the additional training required to become a full fledged SEAL. He admits this himself, stating that "UDTs simply refer to themselves as SEALs due to the restructuring [after the UDTs were dissolved]." Due to the extra training required, UDT =/= SEAL. This is not to say that UDT is less than SEAL, only that the two are not the same. http://www.military.com/veteran-jobs/career-advice/military-transition/famous-veteran-jesse-ventura.html
I don't need to look up civil procedure to tell you about how that works. If you'd like, I would consider sending you my civ pro books from law school so you can study them.
Jury instructions might help you better understand how this all worked out. http://www.popehat.com/wp-content/uploads/2014/07/Ventura-Jury-Instructions.pdf
3a. "The second element is that Mr. Kyle’s story about Mr. Ventura was materially false or, put another way, was not substantially accurate. The story may be substantially accurate even if it contains minor inaccuracies, as long as the substance or gist of it is accurate. Mr. Ventura must prove this element by the greater weight of the evidence (see Instruction No. 7). "
3b. The third element does not relate to the actual truth of the story, but to Kyle's belief of the truth of the story. There is a huge difference between element 2 and element 3. This is the only element requiring a higher burden of proof. I know this one seems easy to read, but it's not for someone untrained. One can reasonably satisfy the burden of proof for element 3 and still not satisfy element 2.
I.e., the story could have been found to be more likely than not, true. However, they could then find that Kyle had serious doubts as to the veracity of the story. This could be due to intoxication, discrepancies in his deposition, etc....
Tl;dr: UDT is not SEAL. Veracity of the story, as you originally posted, is determined by the preponderance of the evidence.