Milly Main died in 2017 at the Royal Hospital for Children (RHC) on the campus of the Queen Elizabeth University Hospital (QEUH) from an infection, which her mother said she believes was "100%" due to contaminated water.
Glasgow MSP Anas Sarwar has been supporting Milly's parents since it emerged they were not told about any link between their daughter's death and contaminated water at the site.
Mr Sarwar was passed information by a whistle-blower showing an outside contractor warning of infection risks at the hospital through its water pipes on three separate occasions.
Now, the health board has reported the child's death to the procurator fiscal, something which the Labour MSP has said is an attempt by management to "look like it is being proactive".
Kimberly Darroch, Milly's mother, has previously called on the lord advocate to hold a fatal accident inquiry (FAI) into the cause of Milly's death through a letter from her solicitors - which also referred the case to the procurator fiscal.
Mr Sarwar said: "Milly's death should have been reported to the procurator fiscal at the time.
"The way her family has been treated is disgraceful, they were kept in the dark for years and shown no respect by the health board when a brave whistle-blower shone a light on the QEUH infection scandal.
"The health board has now decided to refer the case to the procurator fiscal in the knowledge that Milly's parents did so weeks ago.
"It is a cynical attempt to look like it is being proactive when it has been deliberately evasive up until now."
He added: "I'm sure the lord advocate will listen to Milly's parents' demand for a fatal accident inquiry.
"This is a painful experience for Milly's family - it is forcing them to relive her death all over again, nearly three years after her tragic death.
"I will not stop until there is justice for Milly's parents and they receive the answers they deserve.
"The NHS board has lost the trust of parents, patients and the public.
"Those in charge must go - allowing a truly independent investigation so that the truth comes out and something like this can never happen again."
Health Secretary Jeane Freeman has escalated the board to level four on a five-level scale of government involvement in the authority and has told bosses they have "one last chance" to respond appropriately to the scandal.
A spokeswoman for NHS Greater Glasgow and Clyde said: "The death of any child is a tragedy and we continue to offer our sympathies to Milly's family for their loss.
"Following recent concerns from Milly's family, the public interest in her death and discussions with the Cabinet Secretary for Health, we sought advice from the procurator fiscal.
"Following this advice, it was deemed appropriate to refer Milly's case to the procurator fiscal, which we have now done.
"Milly's case is also being considered as part of the review of patient episodes that Professor Marion Bain, director of infection prevention and control, will be overseeing and this will involve Milly's family in whatever way they wish."