0101 GMT December 13, 2018
Prentice Steffen said he was "surprised" he was prescribed the drug, BBC reported.
He told BBC Newsnight the sport's governing body was wrong to give the cyclist permission to use a powerful corticosteroid before major races.
Wiggins said his use of the drug was for legitimate medical reasons and that no rules had been broken.
BBC Newsnight also spoke to the convicted doper Michael Rasmussen, who said that, taken in isolation, the pattern of Wiggins's use of the corticosteroid triamcinolone ahead of major races seemed "suspicious".
The issue of Therapeutic Use Exemptions (TUEs), which allows athletes to use banned substances if they have genuine medical need, has been in the news since dozens of Olympic athletes had their private data stolen from a World Anti-Doping Agency (Wada) database by a group of hackers calling themselves The Fancy Bears.
Dozens of athletes have been affected and there is no suggestion they have broken anti-doping rules.
But focus has centered on five-time Olympic champion and Tour de France winner Wiggins, because of the nature and apparent timing of his TUE applications.
The stolen data revealed Wiggins, an asthma and allergy sufferer, was given permission to inject the banned drug triamcinolone, a powerful corticosteroid, just days before three major races, including the 2012 Tour de France, which he won, becoming the first Briton to do so.
He also received similar permission to use 40mg of the drug before the 2011 Tour and the 2013 Tour of Italy.
But questions have been raised over why Wiggins apparently did not need the drug before 2011, or after 2013.
In 2009, Sir Bradley's only TUEs were for standard asthma inhalers.
Dr. Prentice Steffen was team doctor at Wiggins's former team Garmin Slipstream that year, when Wiggins had his breakthrough in road racing, finishing a surprise fourth in the Tour de France.
Though he could not comment on Wiggins's private medical records, he was said he was "surprised" he needed this sort of intervention.
"I was surprised to see there were TUEs documented for intramuscular triamcinolone just before three major events — two Tours de France and one Tour d'Italia.
"You do have to think it is kind of coincidental that a big dose of intramuscular long-acting corticosteroids would be needed at that… exact time before the most important race of the season.
"I would say certainly now in retrospect it doesn't look good, it doesn't look right from a health or sporting perspective."
Sir Bradley's TUEs applications are understood to have been made by the then team doctor Dr. Richard Freeman, who is now team doctor at British Cycling.
In each of them it states that Wiggins underwent a nasal endoscopy in 2011, suggesting he needed more serious intervention to control his allergies.
Dr. Freeman did not respond to a request for comment.
In Sir Bradley's 2012 autobiography 'My Time', there is no mention of asthma or allergies. Referring specifically to 2012, he states how he was "only ill once or twice with minor colds" and "barely lost a day's training from it".