The standard before your convicted is that the jury must find you guilty beyond a reasonable doubt. The standard after you've been convicted is that you must have found substantial new evidence that warrants reconsidering the verdict, or you must show that the original trial was mishandled somehow. "I think the jury was stupid" is not a valid appeal.
I think this re-raises the "trap door" question.
In this case, up until conviction you are presumed innocent and guilt must be proven. Post conviction most of the appeals process is bared if not filed within 14 days of conviction (it used to be forever but then the US Justice system decided woohhh there that's too long and burdensome on the Justice system so 14 days was deemed a reasonable change to the previous 'forever'. A totally reasonable happy middle). After 14 days from conviction really the only relief available is to prove actual innocence, a much higher and more difficult standard to meet.
With the caveat that this is coming from someone with zero training in law: what a load of horseshit.