Eric, I didn't want to be the first person to respond to this thread! However, since nobody else has, here goes.
I have had a similar experience, though again, as in the related thread, not identical. Just recalled it going through my matches.
My husband and I are from very different roots, me mainly from London and Home Counties, he mainly from Yorkshire and the North.
He is a DNA match with someone who has a private tree, but who has responded to me.
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He matches her and her maternal aunt through one branch of his family from the Birmingham area, they are 5th and 4th cousins respectively.
She contacted me again after looking at my tree and finding that we had a name in common on her father's side, thinking it likely to be on my husband's line again. However, it was on my maternal line.
A married B. After A's death, B went on to marry my maternal 3x great uncle (brother of my 2G grandmother) in London.
There were children from both marriages, who are obviously genetically related to each other, but not to me, though we could have easily ended up so. She is descended from son of the first marriage on her paternal side.
So, she and her aunt are confirmed matches with my husband on her maternal line, she could have turned out to be a match with me on her paternal side as well, but is still fairly closely linked. Also, she is connected to both my husband and me (by marriage, at least). This would put her in a very similar situation to our children and any children you and your wife may have - connected to a match through both of the parents.
I would never have realised if she hadn't contacted me again, as I have no access to her tree.
Regards Margaret