Contribution based JSA for mixed immigration status couple

Hi all, I’m not to sure about this one so I though I’d see if anyone can shed any light on it.

Couple, one a Brit cit, the other a Canadian national with no recourse to public funds but has a right to work. He gets JSA(IB) at the single person rate. She may be entitled to contribution-based JSA through previous work in the UK a few years ago and work she had done in Canada last year (thanks to the UK’s reciprocal agreement with the Canada). If she claims JSA(cb) and is entitled, will this not just count as income for his JSA(ib) claim and they will be no better off? And they can’t make a joint-claim to JSA as she has no recourse to public funds.