The club issued a statement on Wednesday saying there had been "disturbing and inappropriate" commentary on the club's ASADA-AFL inquiry.
Fairfax Media had reported earlier that Hird was warned in late 2011 after investigating the anti-doping status of certain peptides.
Essendon said those claims were "factually incorrect".
"Until the ASADA investigation is completed the full context of this particular meeting should not be the subject of innuendo," the statement said.
The Bombers said Hird had been unable to defend himself from accusations while the club's supplement use in 2012 was investigated.
"Representatives from the club have requested all parties to the investigation to guarantee confidentiality and to afford natural justice," the statement said.
"Breaching this confidentiality directly undermines the trust in the process and selective disclosure of information relating to the investigation appears to be deliberately threatening the integrity of this process.
"For the reputation and integrity of senior coach James Hird to be questioned without the right to due process, is extremely disturbing and inappropriate in the circumstances."
The club also shot down calls Hird was the "initial champion" of the Bombers' former sports scientist Stephen Dank. Dank, the statement said, was introduced to the club by Dean Robinson, the high-performance manager stood down by the Bombers since the scandal broke in February.
"Mr Dank was brought to the club at the insistence of Dean Robinson with whom he had worked previously," the club said.
Essendon reiterated its hope for the ASADA investigation to be completed, and said while it had been limited by what it can say through the process, it had been forced to defend itself against "factual inaccuracies".
Meanwhile, the Australian Sports Anti-Doping Authority has conceded there are "complex" issues at the centre of the Essendon investigation.
"ASADA acknowledges that the issues regarding AOD-9604, alongside a number of other substances, are complex, and it is considering these issues as part of its ongoing investigation," an ASADA spokesperson told AFL.com.au.
The legal status of AOD-9604 at the start of 2012 continues to be challenged by the media, but the spokesman said: "Given the investigation into Essendon is ongoing, ASADA is unable to comment on media speculation regarding possible anti-doping rule violations concerning a range of substances.
"This is because ASADA has a duty of care to be both thorough and accurate in every step of the process.
"Information provided to external parties regarding the status of AOD-9604 in sport is based on WADA's [World Anti Doping Agency] advice."
ASADA's response follows suggestions the lead investigator told Bombers players at a briefing in April 2013 that the chance of them being successfully prosecuted for taking AOD-9604 "was very, very, very low."
The head of the Australian Crime Commission issued a statement on Tuesday night which alluded to the confusion.
"The Australian Crime Commission sought expert advice from the Australian Sports Anti-Doping Authority (ASADA) at the time of developing the Organised Crime and Drugs in Sport report and was advised (correctly) that AOD-9604 is not prohibited under schedule S2 of the WADA prohibited list," ACC chief executive John Lawler said.
"The World Anti-Doping Authority (WADA) is the pre-eminent authority and expert in this field and the Australian Crime Commission welcomes the subsequent clarification by WADA on 22 April 2013 of the status of AOD-9604 as a prohibited substance under the S0 classification."
AFL chief executive Andrew Demetriou would only reiterate the confusion about the status of AOD-9604.
"All I'm going to say is what I said the other day and that is that there is some uncertainty around the status of AOD-9604," Demetriou told Fox Footy on Tuesday night.
"What I don't want to do is pre-empt the outcome of the investigation."
