Since avatars, just like all other human beings, do not have any supernatural powers, and only use the opportunity that come in their way, it is important to analyze the method used by Shri Ram and Mata Sita to abolish Agni Pariksha. It is important to also know the subtle difference between avatar and other human being.
Since God, as we understand, knows everything, HE does have some knowledge as to which path to take, when to take and when to leave that path and chose a fresh one. God knows what result HE wants. But, Karma or action of individuals is NOT in the hands of God. That is where Hindus differ from other religions. We believe that we, as humans, have complete control on our Karma or action. So although God has, should we say, better knowledge and understanding of which path to chose, HE also, is not in a position to control karma of individuals.
In between God as Avatar do come on this earth to correct the path but his efforts, result only in short term correction as Humanity has a strong tendency to move towards destruction. Avatars also sometimes, find themselves in desperate situation, and how the avatar deals and comes out of those desperate situations, usually provides an important Dharm.
A very ridiculous explanation of an event considering the fact that the explanation, itself states that Ram asked Agni Dev for safe keeping of Sita in TOTAL PRIVACY when even Lakshman was not there, and yet Ram asks for Agni Pariksha in public, thereby bringing in a very explosive event in Ramayan, which encourages exploitation of females.