"I didn't get a chance to check other wards but even if it's just ours it needs to be rectified."
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The doctor went on to say herself and nurses had been scrounging around for spare cups and teabags.
"Because how are you supposed to say no when they quietly ask.
She said a hapū doctor had to walk from her ward to the cafeteria to fetch a hot beverage today.
"I will keep handing them out for free until you stop this nonsense.
"[It's] stingy, maddening, infuriating."
The tweet received outrage from hundreds of people, with one health professional saying this had recently happened in Dunedin too.
"Signs up saying you can't even drink from the water filter but to go downstairs to the coffee shop. Water is in the whānau room but that's on the ground floor," the person commented.
Another said: "For goodness sakes. Maybe if they won't pay perhaps the supermarkets could donate some tea and biscuits."
"Wow, that is unbelievably s**t," another person said.
One man reposted the DHB's values - "we see you, we welcome you as a person" - and commended Fu for speaking up about the issue.
The DHB spokeswoman said it was important to the DHB that families and whānau were comfortable and felt welcome on its wards.
Some commenters on Twitter have been saying this is an issue which reflects a poor health system.
The Herald approached Health Minister David Clark's office for comment and were told "it's an operational matter" and the minister would not be commenting.