The former chief executive of the NBN project, Mike Quigley, has released data he says shows NBN Co has perfectly good financial and accounting systems, and cost blowouts are Malcolm Turnbull’s fault.

Quigley has published an extensive essay on the last few years at NBN Co – the corporation behind the big telecoms infractture rollout until 2013 – in which he claims shows that the plan for a ‘multi-technology mix’ (MTM) is needlessly expensive and technically inferior.

“It is time to stop trying to blame the previous government and management for the problems with the costs and timing of the MTM,” Quigley wrote.

The former chief said the government has to admit it “grossly underestimated” the cost and timeframe of its reduced NBN rollout.

The spat started shortly after the most recent federal election, when Mr Turnbull (then the Communications Minister) said NBN Co’s financial and accounting systems were “completely inadequate”, and the estimates for the cost of Labor’s fibre-heavy were way off.

“Immediately after the September 2013 election the company was not even able to accurately tell the new government how much the NBN was costing per premise, or to accurately allocate the costs the company was incurring to its different networks and activities,” Mr Turnbull said in a blogpost in August.

The “financial inputs” from NBN Co that underpinned the 2013 strategic review of the NBN “were inaccurate and later significantly revised”, Turnbull said.

It was his justification for new costings showing that the Coalitions MTM plan would cost up to $15 billion more than originally estimated.

But Mr Quigley has shot back at the claims of financial incompetency.

“Regarding NBN Co’s accounting systems, Mr Turnbull also omits to mention that five years of independent audits by the Australian national audit office and PriceWaterhouseCoopers and a specially commissioned, detailed forensic review by Korda Mentha in 2013 failed to identify any material deficiencies in NBN Co’s accounting systems,” he wrote in the paper published last week.

Mr Quigley said the $15 billion cost blowout was actually due to Mr Turnbull’s underestimation of the cost of his multi-technology mix (MTM) model.

Quigley has released a comparison of the 2013 strategic review (of Labor’s technically superior fibre-based model) and the 2015 (MTM plan) costings.

His data suggests costs associated with rolling out fibre to new and existing have fallen continually, along with costs for satellite and wireless components of the plan as well.

But Mr Quigley says Mr Turnbull continues to talk down the cost of the Coalition’s fibre to the node model, “and now the chickens are coming home to roost”.

“As long as Australia’s broadband future is tied to an aging copper network, we will fall further and further behind our competitors and trading partners. At a cost of $56 billion and counting, that will be Mr Turnbull’s legacy,” he wrote.

Labor’s communications spokesperson, Jason Clare, has lept on Mr Quigley’s claim.

“Malcolm Turnbull has no one else to blame for the massive blowout in the cost of his second-rate NBN but himself,” Mr Clare told Guardian Australia on Friday.

“Malcolm Turnbull promised he could build a second-rate version of the NBN for $29.5 billion and get it to everyone by the end of 2016. It’s going to cost almost twice as much and take twice as long to build.”