How do you guarantee a trial by jury, if an entire jury could be paid actors?
It's a bit silly to worry about that level of conspiracy.
But even if it weren't silly, there are easy answers. An oversight board, or revealing the jurors after the case is decided, or revealing the entire juror pool of 50 some-odd people, etc.
Just release the information afterwards, or notarize something. That's such a trivial problem to solve. How do you "prove" to the defendant that the jury in front of them right now isn't just the DA's extended family and friends?
It isn't just bribing 12, it is bribing them in a short period of time.
If I'm going to do something and want to bribe a judge I have years to research all the judges who might be at my trial (there are not very many). Each will have a different bribe that will work. (one doesn't want his wife to know about an affair; the next is in an open marriage and doesn't care but he has big gamboling debts that you can "take care of"...)