Margaret McCartney has written quite a bit about the downsides of screening.
It is inevitable that if you screen the whole population for something, there will be some that have it, a lot that don't have it, and a grey area in the middle. How the test accuracy and treatments affect the ones in the middle will make all the difference as to whether it is worthwhile.
The old information was too biased about the success of the scheme and the newer information they give you is more realistic.
I got recalled at the last one. They were very thorough and thankfully I did not have to have a biopsy or anything (only a small number of those recalled go on to have this). TBH, the screening staff were not so good, but the clinic staff were the best I have met in the NHS and would have done anything to make sure that there was nothing, and had many procedures to double check. ( They sort of reminded me of the film Mousehunt, where they hunt the mouse with such an obsession that there is no house left at the end
https://en.wikipedia.org/wiki/MouseHunt_(film) ) However, there are a lot of very good people and very good procedures in the breast clinics, that I think they will become increasingly accurate as time goes on.
You are allowed to not accept your invite - you do not have to be taken off the scheme altogether - you can always go to the next one if you want. Whatever you do, you need to be aware of any changes yourself anyway, and see the doctor for a referral if you are worried.