I did pretty through investigations into the trees of both D and A about 3 years ago, but I've fished out all my notes from that time to check through again. Back then I had no shared matches with A and my sister had only D, so it was the obvious place to start. I was then mostly looking for a documented connection as there was no other evidence to suggest I shouldn't be, although from previous experience, I always keep other possibilities in mind. And you have to start somewhere when considering an undocumented connection - otherwise the possibilities are too numerous.
My investigations back then revealed that A and D were descended from a full brother and sister, and that the sister (D's ancestor) married a man with a relatively unusual surname. The matches my sister shares with D do not get top marks for useful trees or responding to messages, but from what I could determine, the shared matches shared ancestry with D via the husband with the unusual surname - hence were not related to A.
Having read the DNA article in the latest newsletter, it may help if I clarify two things here.
1) I am very well aware that we cannot blindly assume that everything written in official records is correct and, as it happens, around 25 years ago I started writing an article, based on my own experiences, of the numerous different ploys our forebears used to cover up their indiscretions. And, as well as deliberate cover-ups, there are also many genuine errors in the records.
2) One of the two main reasons I did a DNA test was to check the validity of my tree, including checking out all my 'cover-up' theories. Mostly, my DNA has confirmed my suspicions that some of my ancestors had been somewhat economical with the truth. And referring to what Helen wrote above, it's not just the neighbours that need to be checked out - boarders, lodgers and housekeepers are also key players to consider.