The Duke and Duchess of Sussex have said they never cited privacy as a reason for stepping back from royal life.
Prince Harry and Meghan's global press secretary said a "distorted narrative" had been created.
It follows suggestions from some commentators that their Netflix series, which launched this week, is at odds with their reasons for leaving the UK.
The statement said this was "entirely untrue".
It said they always intended to keep up public duties after leaving the royal family.
Their decision to step back from royal life in early January 2020 was announced in two coordinated statements from the duke and duchess and Buckingham Palace.
In their statement at the time, the Sussexes said: "We now plan to balance our time between the United Kingdom and North America, continuing to honour our duty to the Queen, the Commonwealth and our patronages.
"This geographic balance will enable us to raise our son with an appreciation for the royal tradition into which he was born, while also providing our family with the space to focus on the next chapter, including the launch of our new charitable entity."
At the time, one interpretation of their decision led to commentary suggesting that press intrusion, particularly that affecting their then-newborn son Archie, may have been a factor.
The couple have engaged in separate legal battles against newspaper publishers, including over privacy, since they told several of the UK's biggest tabloid titles they would no longer cooperate with them.
Press intrusion is a theme that runs throughout the first three episodes of the new Netflix documentary, Harry & Meghan, which is co-produced by the couple.
And since the release of the episodes and two minute-long trailers, some commentators cited in the media have suggested they have changed their tune on the subject of privacy.
For example, Dickie Arbiter, a former press secretary to the late Queen, told GB News after watching the first three episodes on Thursday: "They left because they wanted privacy.
"Well, so much for privacy in this documentary because we are seeing a lot of family photographs."
Another critic responding to one of the trailers was quoted by a newspaper as saying: "They've blown their own protestations out of the water and detonated their own privacy policy."
The Sussexes' global press secretary, Ashley Hansen, said in a written statement: "The Duke and Duchess have never cited privacy as the reason for stepping back. This distorted narrative was intended to trap the couple into silence.
"In fact, their statement announcing their decision to step back mentions nothing of privacy and reiterates their desire to continue their roles and public duties. Any suggestion otherwise speaks to a key point of this series.
"They are choosing to share their story, on their terms, and yet the tabloid media has created an entirely untrue narrative that permeates press coverage and public opinion. The facts are right in front of them."
BBC