After many years of calculating incomes based on federal guidelines, I can certainly tell you that yes, the HUD people would very likely have found out about this big swop of money landing in the participant's bank account. When you sign up for one of the income based programs, you sign away privacy rights, and give them the access to almost all your financial information. It goes with the territory.
Big sudden infusions of cash into your income are very common and are always a problem for such programs. And you're probably not the first person they've had to deal with who claimed this sudden infusion of cash is a gift, a loan, found money, etc. this month. As a society, we have determined that we want this sort of program monitored to the max. So they tend to do it just this way.
They tend to be very suspicious, after all, this could be that this was your share of the drug money, your share of the bank robbery haul, your cash you stole from someone. People rarely "gift" others money, or loan others large sums, especially low income people. People do frequently inherit money, and that's available for you to live on now, so it is generally includable income.
I cringe when I see these set up show type things where the really destitute person is "blessed" by a rich person with a big infusion of cash. I have seen cases of where people refused inheritances, because it will in the long term, mess up their Medicaid and housing benefits worse than it would help them on the short term.
Now, you should appeal this to the next level in the program. You will, before proceeding much further or having any chance of getting things changed, need a clear definitive answer as to why your windfall was considered includable income. You won't get that by arguing with the local person who has done your certification, regardless of how many of their own statutes you cite and quote back to them. The truth is, they do it all the time, you don't. You do not need to cite law, quote statutes or make some brilliant statement. You just appeal through all levels of appeal.
Just remember that the government, matrix of evil, is not out to get you personally, they just have ways they go about things, and believe me, they've seen and heard it before, and they have certain expectations as to how their clients are usually going to behave and finance their lives based on these repetitions of what they've seen. That's what they look for.
It was a very good decision that you have told them about the situation before they found out you got it and called it fraud. Which they were expecting out of everyone and would've been checking everyone for. It may be that they can find it possible, with your explanations, to see it clear to accept your explanations of what happened and change their determination. But then, it's not really likely.
As it has been pointed out, we are not in the position, do not have your very personal exact information and even if we did, we do not have the expertise with this program necessary to explain to you exactly what you have done to cause your gifted/loaned whatever-ed income to be included and your rate to be raised.
And once you have had a decision about your case, as in you were told you'd have to pay more, an appeal must go through the proper channels. So you would, if you get an attorney and fight this, have to know exactly why, according to HUD, you have been refused. What are they calling this money? The Legal aid program in your area may offer you some real guidance about appealing a HUD decision, you should seek out and speak with them. They're the legal entity that deals with a lot of business in this area. I frankly would think you're just going to have to end up paying the extra, but discuss this with legal aid and keep the appeal going up to the last rung of the ladder.