A couple of questions - does the DSFA have all records of this application - identification, copies of proof of residence? If a person was claiming unemployment - do they have receipts from when that person signed on? I'd definately get this one sorted - especially if there another person using your RSI or has other personal data.
If you werent in the country - you should be able to show proof of this ie. passport stamps, and if in employment elsewhere - wage slips, work records, returns to tax etc...rent book, bank account, anything that will show that you werent in the country and it wasnt possible that it was you who signed-on and claimed these payments. That would be my advice. Maybe, go to citizens information as well and get their input.