It is important to understand Allah's promise when it comes to the Quran:
[Quran 2:106] We do not abrogate a verse or cause it to be forgotten except that We bring forth [one] better than it or similar to it. Do you not know that Allah is over all things competent?
[Quran 15:9] Indeed, it is We who sent down "the Dhikr" and indeed, We will be its guardian.
The nonbeliever claims that this verse is referring to the bible. However, when looking at the context, there is no mention of the bible or the people of the book. The subject of these verses is the Quran (see 15:1 and 15:6 which uses "Dhikr" to refer to the message the prophet Muhammad received). And this is Allah's message that indeed he will personally guard this Dhikr the prophet Muhammad received.
[Quran 75:16] Do not hasten your tongue [O Muhammad], to hasten with recitation of the Qur'an.
[Quran 75:17] Indeed, upon Us is its collection and its recitation.
This verse is Allah telling the prophet Muhammad do not worry about the Qur'an, ALLAH HIMSELF will personally collect it and recite it. This is Allah's promise that he himself will personally collect the Quran and recite it. So Allah promised he would collect the Quran and ensure it is recited the way he wants it to be. Allah had an influence in the Quran after the prophet Muhammad just as he promised--and thus Allah is the one who will compile the Quran and put it together. Allah, as he promised, ultimately ensured the Quran we have today is the one he wanted us to have, just as he promised and just as he promised he would protect it (15:9). And in 2:106, Allah said he has the option to abrogate or cause a verse to be forgotten...
So no, the "history" doesn't matter. Most of this so called history is based on Hadith anyway, which as this website has shown time and time again are untrustworthy. It is also based on manuscripts which may have human errors, however, Allah said he himself would ensure the Quran, its compilation and its preservation. So in the end, ultimately, regardless of the history or instances of human error, Allah is the one who compiled the protected the Quran in the form we have today. Allah's intervention was in place to compile the Quran we have today and have it recited the way it is. Thus the Quran we have today is one that was compiled and recited by Allah as he promised it would be, regardless of the errors of humans, in the end, through his complex interventions, Allah ultimately made the Quran the way he wanted it to be (the way it should be) and he will be its guardian. Done. End. Resolved.