Historically, there have been four sources of theology:
This formulation goes back quite a ways. Scripture is always first, Tradition is always second, and reason and experience are a distant third and fourth. The fun comes in when one realizes that it is not possible to read Scripture without a tradition.
As a very banal example, in the Hebrew text, YHWH has no vowels, and yet traditionally the vowels of "Adonai" are used, resulting roughly in "Yahweh" or "Jehovah." The tradition informs the reading.
The position of the Catholic Church is actually quite rational in this regard - it reserves to itself the power to declare what is traditional and non-traditional when reading Scripture. In a way the standard of what is acceptable within the Roman Catholic Church is what the church says.
The Councils are like that, only unlike a single interpretation (namely that of the Bishop of Rome,) the Ecumenical Councils were the best attempt at the time to convene all of the spectrum of Christianity. When, in 325, Constantine gathered the church, the whole point was to get as broad a consensus as possible. The statement at Nicea had no more legal authority or scientific power then a petition signed by, say, 55 leading landowners in the American colonies in 1776. But, the attendants were sufficiently representative and authoritative that it made sense for them to be considered the standard bearers of what "Christianity" meant at the time.
Were they "right?" That's actually a non-answerable question. What they were was representative of what the vast majority of influential Christians believed. Sure, they asked for the Holy Spirit's guidance, and these were good men - but did God actually physically appear and say "This is my beloved council in whom I am well pleased?" No.
But then again, did he ever do that when King James' translators presented their work to the King? Or when Matthew, Mark, Luke, John, and Paul dropped their parchments in the mailbox? No, again.
I believe wholeheartedly that the way the Christian Faith is practiced is both what God intended and still manages to fall woefully short of what is "right." Trust me when I say, of all the indiginities God suffered, his church is by far the most recent. It is a flawed creature - but like a little child it seeks to please its Father as best it can.
As a hermeneutic, Christians tend to put more emphasis on those closer in time to Christ. As a matter of practice, we tend to defer to people better at theology than us (I, for one, cannot take on Polycarp or Irenaeus or Augustine, or even the Bishop of Rome). As an agreed upon set of rules, then we traditionally defer to the traditional interpretation out of traditional accepted theology.
Is it "right"? Who knows. But it is representative of the "standard" against which we measure theology? Indeed, it is the very definition of "the best we can do."