BBC political correspondent Terry Stiastny said the Downing Street statement covered an issue it might not have expected people to ask about in the past.
Our correspondent said No 10 appeared to be aware it might have faced accusations of not being open about Mr Brown's recent hospital visit.
The statement comes after speculation over the prime minister's health.
In a US TV interview last month he was forced to deny suggestions he was slowly going blind.
He was asked by NBC anchor Brian Williams if his other eye was now failing, but insisted: "My sight is not at all deteriorating."
A few days later, ahead of the Labour conference, Mr Brown was asked the same question by the BBC's Andrew Marr, and again denied there was a problem.
Mr Brown was diagnosed with a detached retina at the age of 16 - the result of a rugby injury. He eventually lost the sight in the eye and retained just 30% of his vision in the right eye.
On the Andrew Marr show, he recalled: "I had to have a very big operation to deal with that and every year, of course, I have to check - as I did only a few days ago - that my eyesight is good.
"There has been absolutely no deterioration in my eyesight. I think people should be absolutely clear that although I had problems with my eyes and it has been very difficult over the years, I think people understand that you can do a job and you can work hard.
"I think it would be a terrible indictment of a political system if people thought because you had this medical condition, you couldn't do a job."
Retinal surgeon at Moorfields Eye Hospital, James Bainbridge, said tears very rarely cause serious problems but can in some cases lead to sight-threatening retinal detachments.
Modern techniques can help prevent detachments and when they do happen, they can be treated with "very good results", he said.
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