Labour and the Greens cited Mrs Melhuish's analysis in their attacks on the asset sales programme but her work was dismissed in Parliament by Energy and Resources Minister Phil Heatley and State Owned Enterprises Minister Tony Ryall.
On June 19 Mr Heatley told Parliament Mrs Melhuish had "not included all underlying factors". The following day Mr Ryall said he did not accept her analysis "as I am advised, a number of errors were included".
However, in a June 8 report to Mr Ryall, Treasury said Mrs Melhuish's conclusion of an annual average $240 difference between state-owned and private companies' charges "appears broadly accurate".
In the report released to NewsTalkZB this week under the Official Information Act, Treasury noted that Mrs Melhuish erred by understating the number of customers of Mercury Energy, but said that "does not materially decrease the $240 figure".
In spite of this advice, Mr Ryall told Parliament on June 20 Mrs Melhuish's error "makes a material difference to the weighted result".
Yesterday Mr Ryall stood by his answer, saying: "Advice on the day from both MED and Treasury is that her conclusion is wrong".
But Treasury's advice to Mr Ryall that day was that Mrs Melhuish was just $23 out and SOE power companies charged $242 less on a weighted average basis.
Labour's finance spokesman David Parker said it was "outrageous" for Mr Ryall to claim Mrs Melhuish's figures were wrong "when in fact she was right and he knew it".
Furthermore, Mr Parker said it appeared that National Party members on the finance and expenditure committee which considered the Government's asset sales legislation had voted to report the bill back to Parliament early, "in order to prevent Opposition members getting Treasury advice as to whether the assertion by Molly Melhuish was correct".
The bill was reported back to Parliament more than a month early and just a few days after Mr Ryall first received the advice from Treasury.
Greens co-leader Russel Norman said Mr Ryall's dismissal of Mrs Melhuish's findings, which were similar to those reached his party, were "characteristic of the Muldoonist bullying approach of this Government".
"Anyone who disagrees with them is basically laughed at, put down, or told that they're stupid, yet Treasury were telling that minister that Molly and the Greens were right.
"Mr Ryall should apologise to Mrs Melhuish and to us as well."