Bosses at the German contractor broke their silence after a gagging clause was lifted.
The £776m project is now two years behind schedule and 40% over budget.
Bilfinger Berger is leading the international consortium building the tramline.
Dr Jochen Keysberg, one of the company’s most senior executives, told BBC Scotland the dispute happened because of the way original client Transport Initiatives Edinburgh was interpreting the tram contract.
He said: “Maybe they were badly advised, maybe they just tried to pressure us in a certain position.
“This was frustrating, and if you have a completely different reading of the risk assessment in the contract, you cannot come together.”
Dr Keysberg also insisted that TIE had always been responsible for increases in the cost of the project caused by design changes and problems encountered during utility diversion work.
He claimed the Edinburgh project turned out to be unlike anything the company had experienced anywhere else in the world.
Bilfinger Berger has repeatedly clashed with TIE, the publicly-owned company set up to manage the project.
TIE has frequently criticised Bilfinger Berger, even describing the contractor as “delinquent”.
Edinburgh City Council has now scrapped TIE and work has restarted on key sections of the line.
The local authority’s transport convener has conceded he may not have had the skills needed to help oversee the project.
Councillor Gordon Mackenzie was one of four councillors on the board of TIE.
He said: “I have a social work background, others have electronics and banking management experience, that sort of thing.
“We were not people who had previously had experience of major projects like this.”
BBC Scotland Investigates: The Great Tram Disaster will be broadcast on BBC1 Scotland tonight at 2235.