Many years ago, I heard someone say that the KJV came about because King James I wanted a version of the Bible that supported him getting a divorce. Nowadays, I can't help but wonder how true this is. Thus, I'm asking for the historical reasons the KJV came about.
Since one of the reasons for the English Reformation by King Henry VIII which lead to the creation of the Church of England was divorce, I doubt King James I would have needed a new translation.
From Wikipedia, it sounds like the main reasons for the commissioning of the KJV 70 years after the reformation were around translation errors believed to be in the existing English translations.
The newly crowned King James convened the Hampton Court Conference in 1604. That gathering proposed a new English version in response to the perceived problems of earlier translations as detected by the Puritan faction of the Church of England.
It sounds to me like what you had heard may have just been history getting crossed.
To begin with, that statement is logically flawed as the Bible does not condone divorce — KJV or not.
As far as your actual question, according to Wikipedia it seems like a new English version was proposed "[...] in response to the perceived problems of earlier translations as detected by the Puritan faction of the Church of England."
PS: There also seem to be a recent documentary on the subject, which I've been meaning to see. It seems to be available on Netflix.
The most popular Bible being used prior to the KJV was the Geneva Bible. Unfortunately for the crown, this Bible also contained footnotes of an opposing political nature. Thus the KJV was commissioned with the directive for minimal footnotes. The 1611 text is actually quite similar to the Geneva Bible.