For example, for Catholics the Pope's word is law... unless of course he is an antipope, in which case he was not a pope to begin with, with the rub being that people must judge the pope before he can be found to be holy or unholy.
There are objectively verifiable criteria for discerning the validity of a papal election, and, I might add simply for the sake of clarification, judgments concerning the legitimacy of such an election in no way concern themselves with the sanctity of the papal claimant.
So the pope is the authority, but the people must accept that he is a valid authority before he starts ruling over the people, and if at any time he falls into heresy, it would prove that he was never head the true authority to begin with.
Your first assertion I find somewhat confusing. I would say this; upon elevation to the Petrine See, the Pope ipso facto
'starts ruling over the people', irrespective of their acceptance of his reign.
As for the second assertion, it is not true. If a pope were to fall into heresy (& it is highly debatable from a Catholic point of view whether a pope has actually fallen into formal heresy) it would not mean that he were never "the true authority to begin with". That is simply not Catholic teaching. There has never been an historical instance where a 'pope' is judged not to be such a posteriori
on the basis of his promulgation of heretical doctrine.
Thus the reason that some traditional Christians have come to see the idea of infallibility as a misstep, because no matter how you slice it you still have fallible humans trying to judge, understand, verify, and obey a supposedly infallible authority. It's humanly impossible. And no, it's not theanthropically possible either, unless God somehow overpowers the free will of those in his Church.
Do you not as an Orthodox believe in ecclesial infallibility? I would argue you should, given the presence of this phrase in the Patriarchal Encyclical of 1895: "we are fully persuaded that... every bishop is head and president of his own particular Church, subject only to the synodical ordinances and decisions of the Church universal as being alone infallible". So in any event you have infallibility exercised through the agency of in se
fallible creatures. This is not a matter of God suppressing or overpowering man's freewill; it is an ecclesiological analogy to the Two Wills of Christ wherein the human & Divine Wills remained distinct, yet in perfect harmony. So it is with the Church, Who, whether (in the Catholic view) speaking through Peter (S. Matthew xvi. 19) or through the synod of the apostles (S. Matthew xviii. 18) binds on earth what has been bound in Heaven.