"Would she need to pay over half the house expenses/food out of her separate bank account to prove that she paid for more than half the expenses? "

She would need some kind of proof that she pays MORE than 50% of the household bills to qualify for HOH, which sounds doubtful if theyre living together and he makes more money.  Your due diligence will come into play in the situation, she may not even get much more benefit being HOH over Single, I find that lots of times it doesnt make a difference or not enough difference that Im willing to risk the due diligence penalty.