Following the controversy in the wake of Sunday's Spanish grand prix, Pirelli announced on Tuesday that it will make major changes in time for next month's race in Canada, including reverting to the basic structure of the 2012 tyre.
However, before deciding to make the changes, Pirelli's Paul Hembery had warned that a reaction like that could hand the world championship to Red Bull.
But he now insists: "I know there are concerns that the change will help some teams and punish others. But we are convinced that this is not the case.
"This change has nothing to do with Red Bull's criticism -- certainly the criticism from some in the media was considerably harsher," Hembery is quoted by Speed Week.
Hembery acknowledges, however, that teams like Ferrari and Lotus did not complain anywhere near as loudly, because they were able to manage the original tyres.
"They developed more in the mechanical direction than aerodynamic," he said, "but we do not believe that by making this change, they are going to be disadvantaged," he is quoted by Finland's MTV3.
"We certainly hope not, although there's always a risk. We are still going to be fairly aggressive in terms of choosing the compounds.
"Red Bull never officially came to us and demanded change, which is important for people to understand.
"It is by no means certain that this is going to help Red Bull, so people shouldn't be so quick to assume that," added Hembery.
Red Bull team boss Christian Horner agrees that it is "impossible to predict" how Pirelli's change will change the situation in Canada and beyond.
"It is all part of the challenge of Formula One," he is quoted by the UK newspaper Express.
Referring to the widespread criticism of the Italian marque's approach so far in 2013, Horner said the change for Canada is "ultimately in Pirelli's interests".
"They had to do something for their own image," the Briton is quoted by Germany's Sport Bild.