It does but surely if you are a guest and offer to cook a meal by way of thanks, you don’t just mean “ cook” using food your host had paid for.
Most of us would assume that, but I don't think it's universally obvious. Actually cooking a proper meal is a significant contribution, even if you don't pay for the ingredients yourself.
In a household with a SAHM/W who cooks all of the household meals, would you expect the husband not to appreciate or recognise that huge contribution to the family, on the basis that, although she's the one who puts in all of the effort in cooking the meals, he is the one whose earnings have paid for the food, so she 'hasn't really done anything much'?
It was very ambiguous and I can't understand why you wouldn't say "If you don't have a Co-op loyalty card, could you please take my card and get your points put on it, so that they don't go to waste".
'Use my card' could reasonably mean several things, including 'use it to pay'. She might have thought you were doing a Mrs Doyle-style compromise and saying "OK, then, we'll gratefully accept your cooking our meal - but we insist on paying for the ingredients".
Most Co-ops these days - even the little ones - have self-service tills. These can be ambiguous as well, as SS tills often ask if you want to 'use' your loyalty card when paying, without it being particularly clear whether it means 'use my points on this card TO pay' or 'add my points to this card WHEN I pay'.
Also, she might be used to a bigger supermarket where they combine a credit card and loyalty card in one, so 'using' that shop's card is basically both paying and collecting the points/discounts.
As for those questioning why she didn't notice the big chunk coming off the bill, some better-off people don't really bother to look at totals and just scan their payment card without noticing how much they're paying. She could even have spotted something on special offer (boxes of wine or whatever) and stocked up on it for herself - and thus the differential wasn't nearly as obvious if she was already spending enough to fill the boot of her car.
Some people also have learning difficulties (or are just not very bright) and it wouldn't occur to them to query an amount that most of us think looks obviously wrong.
I think the only two reasonable options are to either let it go or to blame the machine/cashier for assuming wrongly. I really don't think you can assume CFery on her part and go in all guns blazing - especially when you said "Here, use my card".