That is correct. But I put 'mistrial' in quotes because this wasn't a mistrial at all. The prosecution evidence was inadmissible. That's not grounds for a mistrial. This was a simple ruling on evidence (which happens all the time, though in real life would have been addressed before the trial began). If this situation happened in real life the defense would get the evidence excluded, then the prosecutor would free to continue and try to prove the case. If they couldn't meet the burden: not guilty. Double jeopardy rule prevents trying him again.
If judges declared a mistrial because evidence was excluded, you could have cases being tried any number of times, giving the pros multiple bites at the apple and making the double jeopardy clause meaningless. Calling a 'mistrial' because the judge excluded evidence is another reason why this trial goes in the top ten of ridiculous teevee criminal trials.