Let us remember that the knight is in a desperate position. If he can't give the correct answer to his queen's question, he faces possible death as a result. He finds the old woman the very night before he must present his answer in court, and therefore he is driven to distraction by his desire to find the answer that will save his life. Note how he speaks to the old woman that he finds in the grove in the forest:
"My dear good mother," said the knight, "for sure,
I am as good as dead, if I can't tell
what the thing is that women most desire.
If you could tell me that, I'd pay you well."
Therefore, part of the answer has to be that the knight is absolutely desperate to find any answer that will save his life and satisfy the queen. However, at the same time, the answer that the old woman whispers in the knight's ear obviously had a ring of truth about it, so much so, that the knight chose to trust the old woman and present her answer. Perhaps he trusts in her wisdom because of her age, as she herself says to him, "We old folks know so many things." Either way, there is something about her character and the wisdom of her words that leads the knight to trust her and to put his life into her hands.