I do think it an odd rule. Something needs to be done to stop abuse of their services but I'm not sure this is it.
I have used the PDSA once. You have to be in receipt of housing and/or council tax benefits and you take your letter of award with you, it can't be more than 6 months old. That's all the checking they do. So you can use them if you are not on JSA but are on a low income. As far as I know, if you're a homeowner and are claiming JSA you're stuffed because you're not entitled to housing benefit!