They were the first Kiwis to be caught up in the data leak.
The New Zealand Olympic Committee has slammed the actions of Fancy Bears whose sixth release of confidential WADA data affected 20 athletes from 14 different countries.
It said the pair had legitimate exemptions for properly diagnosed medical conditions.
"It is to be expected that some of our athletes will need medical treatment and the necessary exemptions, but what we are concerned about is the illegal releasing of personal athlete information that was held in confidence by Wada," said NZOC president Mike Stanley.
He said athletes should have confidence that confidential information remained out of the public domain but said Drysdale and Burling were not fazed by the leak.
"Mahe and Peter have provided a great example - they have nothing to hide and expect that of all other athletes,' he said.
Before the Rio Games Drysdale said Russia deserved to be banned after the McLaren Report revealed systematic state-sponsored doping and has spoken out repeatedly against drug cheats.
The duo are now on the list of 127 athletes named by the Fancy Bears over the last three weeks.
Among the high-profile names in the latest batch released is Britain's Rio triathlon champion Alistair Brownlee who had a two-day course of acetazolamide in October 2013.
Acetazolamide, or Diamox as it is more commonly known, is used to treat altitude sickness or glaucoma but as a diuretic it has been used by some athletes as a masking agent.
Previous names to have their medical data released in this way include British cycling stars Chris Froome and Sir Bradley Wiggins, American tennis sisters Serena and Venus Williams, British distance runner Mo Farah and Spanish tennis great Rafael Nadal.
The Fancy Bears, who are believed to have targeted WADA's database in retaliation for the investigations that exposed Russia's state-sponsored doping programme, have been widely condemned by anti-doping groups for breaching data protection laws and falsely accusing innocent athletes of cheating.
But their actions have drawn attention to an area that some anti-doping experts have suggested is open to abuse.
- NZN