Having spent time working for the govt. Employment Benefit Office, dealing with complicated cases involving reams of paperwork on a daily basis (including fraud), I have to say that this case comes across as nothing but carelessness on the part of the case worker, bordering on UNCARING.
It's not rocket science to sniff out something that does not quite add up.
Whether or not you have the integrity to do something about it, or simply bin it is another matter.