Dame Sarah Storey and the British Paralympic Association “followed the appropriate process” over a retrospective therapeutic use exemption, British Cycling says.
British Cycling said the report raised concerns of a “breach of privacy”.
Storey, 43, is Britain’s most successful female Paralympian.
She has won 14 Paralympic gold medals including nine for cycling and five for swimming, and is aiming to compete at her eighth Games this summer in Tokyo.
BBC Sport has contacted Storey, who won four gold medals at London 2012, for comment.
The Times reported that she delivered a salbutamol level higher than the permitted limit during the 2012 Paralympic Games.
Storey told the newspaper, through a lawyer, that she had been diagnosed with asthma as a child and had “breathing difficulties” after winning gold in the individual pursuit and used an inhaler before needing to speak to journalists.
A British Cycling spokesman said: “Our understanding is that both the British Paralympic Association and the rider followed the appropriate processes, and that the International Paralympic Committee, UK Anti-Doping and the World Anti-Doping Agency have raised no concerns either at the time or since.
“As one of our responsibilities as a governing body is to give a voice to athletes in our sport, we must raise concerns at what would appear to be a substantial breach of privacy without a substantial demonstration that this was in the public interest.
“One of the reasons why World Anti-Doping Agency [Wada] processes are confidential is to protect athlete well-being so we are particularly concerned by the impact stories like this could have on athletes who may under-use their medicine, and harm their health, rather than risk their private medical records becoming public in the future.”
A spokesperson for the British Paralympic Association said: “We are entirely confident that the correct procedures were followed at the time and have all the relevant supporting documentation.
“It is important to emphasise that just like everyone else, athletes have the right to confidentially regarding their medical records. This is made clear in the World Anti-Doping Agency Code, International Paralympic Committee Anti-Doping Code and from agreed standards in medical practice.”
The International Paralympic Committee said: “With the express consent of the athlete in this case, the IPC can confirm the results from Sarah Storey’s test following her race on 30 August 2012 were uploaded by the laboratory on 5 September 2012 for the IPC, Wada and UCI to view. The case was handled in accordance with the IPC Anti-Doping Code, World Anti-Doping Code and International Standards.
“In sport there are sometimes cases where there are clear explanations as to why athletes return Adverse Analytical Findings. These may involve Therapeutic Use Exemptions (TUEs) which are either already on record or are applied for retroactively in certain circumstances. All TUE applications to the IPC are dealt with by a committee comprising three independent medical experts who assess each case individually.
“It must be stressed that if there are ever any concerns that correct procedures are not followed by the IPC, then Wada, the relevant National Anti-Doping Agency, and international federation – in this instance UK Anti-Doping and UCI – can all appeal. Almost nine years on since the athlete provided the test, none of these bodies have expressed a concern with the procedures followed in her case.
“In addition, the IPC is concerned by the unauthorised disclosure and publication of the athlete’s confidential medical information and reiterates that any concerns should instead have been raised with the appropriate bodies (which they were not).”