A gross simplification, based on very little study, I’d suspect.
Sometimes when people lie to you at a young age, you never think to revisit what they’ve said. This one is a particular piece of bullshit that Protestant ministers tell kids in school to explain why their brand of invisible-man-in-the-sky is better than Rome’s brand of invisible-man-in-the-sky.
There has never been a prohibition on reading the Bible within the Catholic church, only one against using quotations from scripture to promote "heresy" (i.e., whatever disagreed with the Church’s official doctrine - but the Protestant Churches have no high ground to stand on here, when you consider how the text of the Old Testament has been abused to persecute pretty much everyone who wasn’t a straight white Protestant at some point or other).
The truth is that the Bible itself is just not that important within the Catholic faith - certainly not to the extent that it informs Protestant belief. The Vulgate (the Latin translation used since the 5th Century) was always freely available in Latin (or as freely as you could get any book before widespread printing), as were many translations into vernacular languages. The difference was that those translations were for study, not worship, and the Latin Vulgate, the Church’s official bible, was always the source - for better or worse, the Catholics thought that only the Latin Vulgate was sufficiently accurate and “holy” for use in worship.
The Protestant Bible translators (Tyndale in English - Henry VIII’s Great Bible and the King James so beloved of Americans are mostly Tyndale’s work) went to the earlier texts that had been translated into Latin to produce the Vulgate for what they believed would strip away the errors of the Catholic Vulgate. It was an interesting exercise, but it didn’t reveal any grand conspiracy on the part of the Catholics to distort the (reported) word of God - when it comes to instructions for believers, there’s piss-all difference between what the Vulgate said and what the direct translations did.
I was raised Catholic, but I am Athiest/Humanist.
I recommend
A History Of Christianity: The First Three Thousand Years by Diarmaid MacCulloch if anyone wants a good, but sometimes dense, account of how the various branches of The Jesus Club ended up where they are.