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Actually, what the law says is that YOU have to use true and accurate information in order to collect these benefits and that if that information changes you are required to change that information. If you don't, that's evidence of fraud.
From there, they can charge you, which apparently they have done, and your remedy would be to retain a criminal defense lawyer and fight the case, all the way to trial if necessary. You can show your lawyer the information you have which would show that the government actually owes you and not the other way around. You could show that your unemployment had stopped, and explain why you didn't add your boyfriend to your residence information. All of these facts would go to try and show that you had no intent to defraud the government and owe them no money. If the DA cannot prove intentional fraud beyond a reasonable doubt, you could not be convicted of this crime.
Otherwise, the typical penalty for this is probation and restitution to the government. If you wer looking to dispose of it with a plea agreement, although you'd get a payment plan to return the overpayment, you'd typially be able to avoid jail or prison.
The DA is correct. You can be charged with fraud whether their figures are wrong or right, because you did not give them accurate information. The figures do matter, of course, as to how much if anything you owe, but it doesn't excuse you from not disclosing the fact that you moved in with your boyfriend who was, in fact, drawing some income.
California explains how they calculate your benefits here.
For purposes of the criminal case, the DA deals with the information on the application you submitted. For purposes of your defense, you would calculate the payments based on what you should have but didn't submit and use your results to show that you never intended to defraud the government.