In my experience very few non-Jews have any idea of the level of care that is used in making copies of the Torah.
Here's a little info for anyone interested:
Accuracy of The Torah Text | Bible
That's all there to prevent people messing up copies and introducing error in the texts. And given the manuscript evidence, it seems to be pretty effective too.
Not just that -- Christians have had their own copies of the Torah for the past 2000 years. Even if a Jew wanted to go edit the Torah sometime in the past 2000 years, um, good luck with that. You think the Vatican library will even let anyone in, much less give them an opportunity to mess with every manuscript of the Torah they have? Would Jews be allowed into Christian places like monasteries and have had access to do this?
Well, that would be a neat trick.
Even with a transporter from Star Trek to give you instant access to texts that are locked up and unavailable, you'd still have to have people who are excellent forgers and know multiple languages, because for nearly 2000 years the Torah has not existed only in Hebrew.
By now it's been translated into nearly everything, including Klingon and LOLcat...oh my I just Googled and sure enough someone wants to translate the Bible into elvish.
The time required to get to all these copies in all these languages and not have people notice their Bibles have gone missing or been replaced would be astronomical.
Now for fun and mental exercise I should go calculate (roughly speaking) whether the sun might go nova before such a task could be completed.