I have heard that, too, but do you have any evidence to back it up?
The evidence is very logical evidence, and that is the study of the Arabic language and its development.
First let us look at what the Muslims themselves believe, according to Muslims, the Qur'an itself as a book never really existed in the days of Mohammad, rather it was memorized, and instead it was written on any objects found near by such as pieces of leaves, stones, parchment or leather, and so on, not only that, but they were also written by men who Mohammad chose, not by Mohammad himself, it wasn't until after the death of Mohammad that the Qur'an was put into paper.
Now let's look at the logical respond to why the Qur'an must have been rewritten at least more than once, the first thing we should look at is the Arabic alphabets, if you compare modern day Arabic to the Arabic of the 6th century, they are nothing a like, in fact, if we take an Arabic text from the 6th century and post it on this website (Which I will in a second), chances are hardly anyone will be able to read it, also let's not forget that the Arabic alphabets are not Arabic, they are Aramaic originally, and they come from the Nabatean Aramaic alphabets, this is a fact.
Now that we got the origin out of the way, let's look at how Arabic as an alphabet has changed, if you know anything about Semitic alphabets, you'll know that the original alphabets are known as Abgads, (Because they start with Alaph, Beth, Gamal, Daleth, and so on), Arabic on the other hand is no longer an Abgadi alphabet, because it no longer retains its original roots, instead, the Arabic alphabets have been tweaked with a lot after the death of Mohammad, and went through a major evolutionary change (Which was a good change for the language, but not for the history of the religion), so this let's look at these changes:
a) Arabic during Mohammad's days did not have dots, for those who know anything about Arabic today, they know that there are many dots that actually differentiate between letters, for example the letters 7(H)aa', Khaa', and Jeem all look like the same without any dots, but in reality they all produce different sounds and depending on where the dot is or not, you get a certain sound out of it, same goes for other letters such as Baa', Taa', and Thaa', also Ayin and Ghayin, also daal and dhaal, raa' and zaay, and so on.
So from this, we know 100% that the Qur'an has been rewritten at least once, because clearly the Arabic of Mohammad's days must have been very different and there was no dots, the question is who put the dots on the real Qur'an and how do we know there are no errors there?
b) The development of the dots was finalized during the 8th century (2 centuries after Mohammad), the next thing is the vowels, which are very very important also, vowels in Arabic were in development during the 8th century but were not finalized until the 9th century, and they are important because sometimes a word can mean different things depending on the vowels put on it, for example there's a word spelled with kaaf-taa'-baa', or to make it short k-t-b, this is the root for "To Write", but this word depending on the vowels can either mean "He wrote", or "It was written", or "Books", but depending on which vowels you put in there of course, so once again this ensures us that the Qur'an was once again modified for a second time.
I would say the oldest Qur'an that resembles modern Qur'ans comes no earlier than the 9th century, 3 centuries after Mohammad, so to claim that Islam has the original book unmodified is a big major false statement that does not match history, finally, wait for me to reach 15 posts so I can post pics from links and compare between the two Arabic writings, this should be in no time, so wait for an hour or so