Muslims don’t permit Christian Bibles because they have their own version. You should not, however, be unaware of Muslim reverence for the Old Testament. Here is a reference I found without expending a lot of time in the effort:
If there is one assertion that can safely and accurately be made about the Muslim view of the Bible it would be that there is no one unified Muslim view of the Bible. The truth is that Muslims and their scriptures often differ on this subject. Additionally, Muslims differ with one another concerning how to view the Bible.
Some Muslims kiss the Injil [Gospels or New Testament] which the Christian offers them and read it with reverence. Some Muslims forbid their fellow-Muslims to accept it. A few Muslim fathers beat their children who read it. Still other Muslims may burn it or tear it to shreds. Some Muslims receive it politely in order not to offend their Christian friends, but inwardly old it in contempt. Some Muslims, who sincerely desire to read it, read it in secret, lest other family members taunt them for reading it. (1)
The wide spectrum of variance in the attitude towards the Bible among Muslims comes in large part from a tension between what the Quran and Hadith teach about the Bible, and what the Bible teaches about Muslim doctrine. More specifically, the Quran and Hadith teach that Muslims should accept and read the Taurat (Torah) and the Injeel (Gospels) as authoritative revelation from God. The difficulty for Muslims is that they know (or have been told) that the Bible (especially the Injeel) contradicts Muslim doctrine by teaching things like the deity of Jesus, the Trinity, the crucifixion, and the resurrection. So in light of the many exhortations by Muhammad the Prophet of Islam to read and accept the Taurat and Injeel which are known to contradict the Quran, the Muslim logically arrives at the apriori conclusion that the Taurat and Injeel must have been corrupted since the time of the Prophet.
http://www.givingananswer.org/articles/muslimviewofbible.html
Don't believe everything published by muslims on the internet...much of it is aimed at obfuscation and white wash.
Reading the Word of Yeshua is extraordinarily dangerous for muslims and I cannot think of any case, in any muslim country or in any country for that matter, where it is permitted...much less encouraged.
Why do you think there are no Bibles or churches in Saudi? If you believe it is because they have their own version of the truth, you are naive.
The Bible and the Word of God are incredible threats to them. Ask any missionary who has toiled for the Gospel in a predominately muslim country (they often lose their noggins for the very thing you think muslims revere). Ask them if the Bible is viewed with reverence.
Many muslims who have converted to Christianity first came to know Yeshua by reading the Bible. Believe me...it is not held in reverence by muslims.
Your entire premise of Obama not being muslim because he dissed the OT is quite bizarre...first time I have ever heard ANYONE make that claim.