Axiomatic foundations of faith

Perhaps the title could be rephrased, but I don't know a better way to explain my question except in terms of what I've learned in Math and Computer Science. Sometime back I watched some videos from an Orthodox catechism course. During the first lesson of the course, the participants were asked to accept the authority of the church. All subsequent lessons would be based on the participants having accepted the authority of the church to interpret scripture etc for them. I encountered a Protestant sect. They have some unique positions on some biblical issues. What struck me most was that they too claimed that their leadership were the only ones allowed to interpret scripture. What really got me is that instead of making the authority of their leadership the first issue presented to potential members on the first day of their study course, the sect waited till the last day to bring this issue up. Am I fussing over petty things? Because it seems dishonest for people to approach me on the street or elsewhere and tell me "the bible says X" when we've not agreed on a framework for biblical interpretation.