The Sage of Main Street
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"Experts" Are a Cliquethey are religion driven fanatics.
al-Qaida is literally "the base". It considers itself the root of Islam. All other practices are heretical. (takfir)
You're using "base" to mean "headquarters, foundation, root, source." The reason sympathetic specialists on Islam refused to translate it that way is that it implies that Islam is fundamentally a religion of human sacrifice, as portrayed in Apocalypto.