Nicky Stevens' suicide after he left the DHB's mental health facility unescorted against his parents' express direction in March 2015, was ruled avoidable by a coroner in December.
However, after his family asked for compensation the DHB requested the Solicitor-General appoint a new coroner to "conduct further inquiries".
The move was a u-turn that Stevens said blindsided the family, who, until then, had been assured by Webb and interim chief executive Derek Wright that the settlement process would continue.
"It left us gutted, and thinking how wrong we were to believe that the DHB were going to act with mana.
"Your representatives did not even have the courtesy to discuss this complete turnaround face-to-face with us.
"For our whānau this has been a major breach of faith, and flies in the face of the DHB's stated values."
Stevens said because of the DHB's actions they had already needed to seek legal advice and she criticised Webb's original suggestion a request for funding was premature.
"[The DHB] has directed us to communicate via our legal counsel ..."
Webb and Wright, along with the board members, remained silent throughout the presentation.
The request for funding would be discussed by the board at a later stage.