You said you were getting SSDI as 1/2/12. There is a 5 month wait on SSDI benefits, so that is why you did not get a check until May of 2012. That said, if you were eligible for the SSDI benefits in January, that means that you were unable to work in those months (and also, you filled out an application for SSDI, stating that you were not able to work). So there is a disconnect between what you were telling unemployment (that you were ready and able to work) and what you told the SSA (that you were unable to work).
So even though you did not actually receive any benefits until May, you were still "disabled" in January. This is why Unemployment wants a refund of the money you were paid (because you were not able to work, so you should not have been collecting benefits).
That said, you may be able to get out of it. You will have to bridge the gap between the two applications, you can argue that you did not know for sure if you were legally disabled, and that you thought you might be able to do some type of job, even if you would not have made it very long... you were willing to try. Your doctor's opinion can reflect that although you would have difficulty doing certain activities, he does not have the knowledge of the workplace to know if there is any job you could have done.
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