Prosecutors will argue exactly your point, that no innocent person would take a plea deal or confess to a crime they didn't do. But lots of research is demonstrating the opposite. Keep in mind that once police and prosecutors believe you probably are the one who committed the crime, they will usually stop investigating any alternate theories or people, and only focus on building their case against you - and sometimes, even withhold exonerating evidence. So if you do choose a trial, everything that is presented will be pointing at you and you alone, you can try to raise an alternate theory but nobody in authority will back you up. It's a very difficult spot to be in.
No doubt it's difficult, and in countries like Russia it's downright impossible to defend your innocence successfully under such circumstances. But I think if you ever find yourself in such a situation, you have no choice but to stand on the truth, on principle. It's better to go down fighting than to submit. And in game theory terms, there is at least a potential upside to fighting the charge, even if the potential downside is worse. There is no further upside to pleading guilty to something you didn't do.
I'll tell you this... the judge could tell the jury to ignore it, or declare a mistrial, but if someone had offered me a plea bargain for something I was innocent of, I would tell the jury that I'd refused it. Whether that was stricken from the record or not, at that point you're a political prisoner and you've done all you honestly can.
