The New Zealander is due to arrive in Scotland next June to take up the role as former Dark Blues boss Andy Robinson's permanent successor. The 51-year-old revealed he had been in discussions with the SRU "for months" about his new job but Clermont Auvergne, his current French employers, say they knew nothing about the move until Monday's announcement.
That led some commentators to suggest SRU chief Mark Dodson had gone behind the backs of officials at the Top 14 outfit to land Cotter but the Murrayfield boss rubbished those suggestions. He told Press Association Sport: "At the end of the day we spoke to Vern about a contract that begins after his contract with Clermont ends."
Dodson added: "So this is not about enticing someone to break a contract. We were prepared to honour his contract and we still are today. If Vern doesn't turn up until June 2, 2014, that is what we have planned for and are entirely happy with that."
There were suggestions on Wednesday that Cotter could take up his new job earlier than expected after Clermont president Rene Fontes claimed he had tendered his resignation.
His comments came after Cotter - who led the side to the 2010 Top 14 crown and the final of this year's Heineken Cup before losing to Toulon - gave an interview to French paper La Montagne saying he regretted "trusting two or three players" in that defeat to their French rivals.
Fontes told L'Equipe: "I learned today of the interview given by Vern Cotter to the press. The words of our coach had me stunned and deeply disappointed as they were the opposite of his usual behaviour towards our players and our club.
"That same day, Vern told me that after his statement he was offering his resignation. I have taken note of the proposal and agreed to convene the board of directors of the club on Monday to decide on this."
Cotter has denied making any resignation offer and Dodson was equally bewildered, saying: "This is news to us. It broke an hour or two before we held a press conference to unveil Vern. We were as taken aback as anyone by this. We need to try and find out what has been said and then allow events to take their course. But this is nothing to do with the SRU.
"We have to wait and see what happens after this has all been cleared up. I don't know what has been said and who has said it. At the moment this is something that is between Clermont and Vern."