No, the believers of the bible and quran chose not to agree and also chose to avoid the word "possession" while fundamentally relying on the concept for their beliefs and to peddle their belief that it is inspired.
Please, tell us more about how spirit creatures wrote books. Why can't they now send tweets or write facebook posts to clarify things?
It wasn't a matter of choice, the explanation of, "inspiration" is clear in scripture. And it doesn't agree, and is easy to comprehend with the full harmony of whatever example you want to use from either book.
As far as your last statement, it's because clarification is unnecessary. The bible is no longer outlawed amd locked away by the church, anyone can read it and see what it says. The question then becomes will they except it's message or what someone else says its message is?
if a person denies this message, Christians teach they will die. I disagree, this is not what it says. It says the judge is Christ, and that all those who do good and are righteous will be saved. I would argue for example, that persons such as yourself have very valid personal reasons for hating religion and for deciding to have nothing to do with it or its sources. However this does not make you unrighteous, and it is not condemning you especially because what you've done, really, is deny the false christs - which is actually what it directs us to do. Any spite you feel toward the bible is not without reason, and is because of those people.
So unlike most who call themselves Christian, I feel, personally, that if I can see and understand yours as well as likely others reasons for dismissing everything loosely connected to religion, certainly an immortal, just judge called the Prince of Peace can. I have many friends who are genuinely good people who feel similarly to both yourself and cofty, and of these friends I would say if God could judge them unrighteous then we are all royally screwed.