So the Geneva Bible didn't rewrite anything, it's just another interpretation battle regarding 'Calvinism' vs Vatican politics vs Anglicanism then, and not anything to do with translation accuracy.
Translation accuracy when discussing scriptures is a never ending battle....mostly because of two factors.
The Bible was originally written in a manner that was extremely compact that stated a LOT of information in a very few words. (Paper and ink were extremely expensive and books even more so)
Then you have English as a receptor language which has very little of the same grammar or parts of speech or vocabulary.
Idioms and metaphors? Nada!
So unless you are immersed in cultures from 2,000 to 5,000 years ago on the other side of the planet....it's not going to be easy to understand or translate. There aren't many equivalents available.
Then everyone has their own ideas about translating as English is used across a LOT of geographical areas....each with unique ideas about which words carry more weight or less as time marches on. (English is a living language and the original languages of scripture are dead...except for modern Hebrew)
Before the invention of the printing press hand copying was how things were done and copyist mistakes happened. Wealthy elite usually were the owners of bibles in those days. The Geneva Bible was the first of its kind that was affordable for the common man. It was stable spellings and the same for everyone and notes were clearly notes instead of viewed as scripture itself. (Which happened with hand transcription)
The LXX and Latin Vulgate Bibles all varied greatly among themselves....but enough of them together brought to light what was original and what was added as notes in Priest's personal copies they had copied themselves from another priest's Bible.
Some of the manuscripts collected from Syria, Egypt, and Masoretes have added to the accuracy over the years. Including such copies from Dead Sea Scrolls and Siainiticus. Also from other writings that include quoted scriptures.
The Bible we have today is probably as accurate as the autographed copies....they have done their best. But what is truly remarkable....there aren't many differences between a modern Bible and your Geneva Bible. The scriptures have been preserved.