"Using reusable bags for brand competitiveness? What if I go to Countdown with my NW bag and they want to swap it out? (Hypothetical, I've def taken NW bags to Countdown)," she wrote.
She said she spoke with the store owner who said he was "concerned that his staffer didn't follow store policy of asking about swapping CD to NW bags".
"Also said she should have packed it anyway. It's all about the branding. He refused to engage on reduce, reuse, recycle.
"Said 'at the end of the day, I'm not having another supermarket's branding in my store'."
However, the Foodstuffs spokeswoman said the staff didn't put any groceries in the bag because they didn't need to, "her other bags were sufficient", she said.
The owner contacted the woman directly, after talking with staff, and none could recall talking to her about its store policy and not being allowed to use competitor's bags.
"I can't share the content she sent us for privacy reasons, but that version of events, appears to be quote different to her Twitter post," the spokeswoman said.
The store's policy was to "categorically" pack any bag/box provided as long as it was clean and serviceable but was up to the individual retailer to replace with a new one if needed.
"What's more, in the event that anyone at the checkout believes a bag isn't up to standard they will actually give, for free, the customer a new one – for food safety and health and safety reasons.
"So, in a nutshell, the store goes out of their way to do the right thing by the customer," she said.
Progressive Enterprises general manager sustainability, Kiri Hannifin, said Countdown supermarkets didn't "mind at all what bags our shoppers use or where they come from".
"We love Kiwis bringing their own bags - that's the best thing for our environment."
The company was "absolute priority" was to remove plastic wherever it could.
"Then reduce and recycle. Our focus has been on removal."