The fact that someone is found not guilty does not mean they didn't do it, just that the case against them is not proven by the prosecution beyond reasonable doubt.
Wrong. There is no difference between not proven and not guilty. Both are acquittal. Historically, the two verdicts available to Scots juries were that the case had been "proven" or "not proven".
The burden of proof is on the prosecution as a defendant is innocent by default. And has to be proven guilty against any doubt. If there is any doubt then the case is "not proven".