sheker false - Didn't Joseph's brothers volunteer information about their family?

When Judah tells Jacob that Benjamin must be brought to Egypt if the family is to purchase more grain, Jacob asks his sons why they had to mention the existence of a younger brother. Their response is that they were directly asked:

The man asked straitly concerning ourselves, and concerning our kindred, saying: Is your father yet alive? have ye another brother? and we told him according to the tenor of these words; could we in any wise know that he would say: Bring your brother down? (43.7)

However, to me, it sounds like the brothers volunteer this information after being accused of being spies by Joseph (42.7-13). (Shortened extract below.)

And Joseph remembered the dreams which he dreamed of them, and said unto them: 'Ye are spies; to see the nakedness of the land ye are come.'

And they said unto him: 'Nay, my lord, but to buy food are thy servants come. We are all one man's sons; we are upright men, thy servants are no spies.'

And he said unto them: 'Nay, but to see the nakedness of the land ye are come.'

And they said: 'We thy servants are twelve brethren, the sons of one man in the land of Canaan; and, behold, the youngest is this day with our father, and one is not.'

Am I missing something here, or are the brothers fudging a bit of what happened?

Answer

The Art Scroll commentary deals with this and explains that the pesukim as written do not give every word spoken. Consider that they had to arrange to purchase enough food for everyone (including Binyamin's children). Also this teaches the lesson for the future (Just answer the question as asked, do not volunteer information)

Since the obviously unfriendly viceroy had not asked if they had any brothers at home, they should not have volunteered it (Haamek Davar). They defended themselves against Yaakov's charge that they had loose tounges (Akeidah), saying that Yosef had questioned them exhaustively, but not in such a sinister way that they had reason to fear the consequences of a full response (Alshich).

Another point is that the medrash states that they entered Egypt from "different gates" so that the only way they could keep their stories straight was to tell the truth (besides not being good liars). Thus the information was already in the records and they were trying to defend themselves against a charge of spying.