I use a topeak trunk bag, i put it in the child seat in the shopping cart, havn't been bothered yet. It's no bigger than a large woman's purse and much smaller than a diaper bag. I've even shopped with my panniers attached to the side of the shopping cart. I've done both of these at different stores. Maybe it's just that I'm in laid-back california...

Next time could you explain to the manager that you called corporate and that it's manager's discression. Then offer to let him search the bag right now (upon entry to the store) for bombs, and after checkout for stolen items. Then ask "I think that's a fair compromise, don't you?". The manager does have the duty to keep the place safe for his customers and also to make sure that people aren't stealing, but I think it's also reasonable to allow a backpack in the store if they can be assured it's not a safety or theft issue.