(1) I have thought often about the problem you state here, while reading many a question at IPS.SE:
How do we know OP is giving us a fair and objective narrative?
How do we advise OP without getting the other person's perspective?
This is a limitation of this type of site but I don't think it makes our responses ineffective. Yes, we must accept that it is just not possible to verify OP's objectivity or get the other person's point of view. So we (usually) write answers based on the assumption that OP is giving us a true and balanced picture.
(2) May I give my impressions on another approach, as suggested by @Hamlet's answer:
Assume that the account is biased. Assume that details which make the OP look bad have been left out, that dialogue has been misremembered and changed, and that the other parties in the dispute would disagree with how the OP characterized the situation. And then help the OP, and help the people who will find the question later using Google. --Hamlet
In this case, we shall have to 'second-guess' every OP at every point but we can still write good answers that might possibly have to consider providing alternative solutions for at least 2 scenarios -- (1) OP is somewhat misrepresenting things unintentionally (2) OP is strongly biased; the other person is more justified. This approach yields good answers if the member writing the answer is emotionally perceptive and rich in life experience so as to understand where OP is getting biased in the narrative.
(3) I strongly agree with the answer of @Shog9 here as the most sensible and efficient practical compromise between the two very contrasting approaches of assuming OP is presenting a true picture and assuming that OP is biased:
In short, barring questions where we have good reason to believe that the entire question was fabricated for the author's amusement, we should work with the facts presented to us (and ask for more if those are insufficient!) - but be willing and able to question the conclusions drawn from them. --Shog9
In my opinion this is a balanced approach to the problem of reliability of the questioner. We could never be sure of the accuracy of the narration but it seems much simpler to go with the facts "as presented by OP" and still indicate that there is room for other interpretations of the situation.
Good answers will surely help future readers, but if OP has been knowingly or unknowingly presenting a biased perspective, these good answers may not help OP.