Why did Sri Rama banish Lady Sita when he was a witness of her fire-test himself?
I will try to answer your question despite the comments pointing to a certain other answer.
It is not about justification, but about decision making. If there were rumors about Sita Devi then that could potentially reduce respect to her king by their subjects and eventually lead to lesser able administration. As a king, Rama had to sacrifice his personal life for his role as a king - but it is to be remembered that for the rest of his reign, he did not think of another woman either. Which is what makes him so admirable.
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