As I do not work in the Federal Office, I cannot tell you for sure how things will turn out. I can tell you my best guess from your description of the conversation.
You are correct that you made a mistake. When dealing with federal benefits, it is always best to be open about your situation. You would not want them to award you benefits and then later learn that you had not qualified, and then they will sometimes demand the value of the benefits back. This happens often in Social Security.
The fact that you actually qualified for food stamps, combined with the fact that they now have all of the information, leads me to believe that you will have no further trouble.
If I were in the place of a food stamps representative, I would not pay out benefits and then investigate or penalize later. If I had a problem with you, I would simply deny you benefits right from the start.
My guess is that you are just fine and can stop worrying.
As may be stated elsewhere on this site, my comments should not be construed as legal advice. Until I have signed an attorney fee agreement with you, I do not represent you. Reviewing comments by attorneys on any website can be helpful, but should not be considered a replacement for representation by actual legal counsel.
I agree with Mr. Prigmore.
When dealing with any agency that is providing you with assistance of any type, you should always disclose everything and let them determine what is and what is not relevant.
As Mr. Prigmore stated, the worst thing is to not provide information, whether it is intentional or accidental, that is later determined to be relevant and then you have to pay back money and/or have criminal charges brought against you.
With all of that said, I also agree that you should be alright because they do have all the information and you were approved for the assistance.