"A reaction like that would be welcomed by anybody who is concerned that there have been breaches in the system," Sir Craig Reedie told BBC Sport.
"I would always regret the athlete not taking part for reasons other than illness or injury.
Sir Craig Reedie will become Wada president in January
"But if that helps Jamaica to reinforce what they've got to do, and to be much more effective, then maybe her actions will be of considerable help to the fight against doping in sport in that country.
"People will say that we need this to be better. It's happened in other sports. Leading athletes have said: 'We think you should be doing this better.' And that becomes a pretty compelling argument in favour of improvements to the system."
Double Olympic 100m champion Fraser-Pryce spoke out as Jamaica's drug testing programme faces a crisis.
Six of the Caribbean island's track and field athletes have tested positive for banned substances this year, including former 100m world record holder Asafa Powell and Sherone Simpson, an Olympic relay gold medallist at the 2004 Athens Games.
Former Jamaican Anti-Doping Commission (Jadco) executive director Renee Anne Shirley then revealed that the agency conducted just one out-of-competition test in the six months leading up to last year's Olympics.
Fraser-Pryce - who has been shortlisted for the International Association of Athletics Federations (IAAF) world athlete of the year award - said those comments "hurt", and added that she was in advanced talks to set up a union in Jamaica to give athletes a voice and to offer support and education from 2014.
United States Anti-Doping Agency (Usada) chief executive Travis Tygart has described the Jamaican testing system as "an injustice to the fairness of the sport".
But Reedie, who will succeed John Fahey as Wada president in January, said: "He's being a bit hard. I know that they've had difficulties. I think they're determined to resolve the issue and steps are being taken to do that.
"It doesn't seem to me to be totally responsible or helpful to turn round and say, 'It's a complete shambles,' without taking action to do something about it, and they're doing that."
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