Having been an Age Concern (now Age UK) benefits advisor for over 10 years, I think it is highly unlikely that any of their advisors would put anything down on the form that was not true.
What does happen is that many people do not realise quite how disabled they are because their disabilities come on slowly and are expressed in terms of what they cannot do. 'needing help in the garden', need help in the house'.
But if you need help in the garden, it will be because your arthritis means you cannot bend anymore, or you are afraid of falling and not being able to get up again and there are probably other things you do not do that you do not notice, or minor changes you have made in your life, because of stiffness The same with cleaning.
One of the first questions the AA form asks about is getting in and out of bed. When a client told me they had no problem, I would respond,'So you leap out of bed like 20 year old.'. The client woukd say, Oh no, First I have to sit up in bed and wait a bit, then I manage to get my legs over the side of the bed and rest, then I lean on the bedside table to help to stand ..........'
Now someone in that situation does not need a carer coming into the house, But clearly struggles to get out (and into) bed and in an ideal world could do with an Aladdin's Lamp they can rub, and a carer pops out to lend them an arm for a minute or two before popping back into the lamp again. They might be glad of some help getting down stairs (remember a stair lift is an answer to a problem, it doesn't mean you do not have problem.), just for a minute or two.
Anything you do or do not do now that you did or did not do when you were younger and fitter, is likely to be because you cannot do it anymore because of the problem of an aging body.
Time after time I had clients like Ex-dancer who were simply unaware of the problems they had, because they came on slowly and they made adjustments.
So ex-dancer, go to Age UK and ask them to explain their responses on the form and before you go ask yourself these questions. What physical problems are the cause of you needing help in the garden and in what way do those physical problems affect everything else you do, from getting out of bed to moving round the house, to the actions you take to protect yourself from falling.
I reiterate, I think it is highly unlikely that what is written on the form was wrong, more that, you had not realised how much the problems you have doing the gardening/shopping were limiting and restricting the rest of our life, you had just adjusted yourself to them gradually without thinking about them.