Melba, I don't think you are correct in saying 'YOU have to match a shared match at a minimum of 20 centimorgans, and also the match at the top, ALSO has to match that shared match at 20 centimorgans or more or the shared match won't show up.'
I have several examples of shared matches sharing less than 20 cMs with either me or a decent match.
I don't know their exact criteria, but it seems to be if two of the shared matches are closely related, then they will sometimes show up with a third match, even if they share less than 20 cMs.
For example, me and my first cousin share 723 cMs.
She matches with someone at 25 cMs, I match them at 15.2 cMs.
We show as shared matches with each other.
My third cousin and I share 153 cMs. Her daughter and five of her daughters (third cousin's grandaughters) have also tested. One of the grandaughters shares 7.7 cMs with me.
Shared matches for third cousin, this grandaughter doesn't appear, though the other 5 family members do, plus several more matches.
Shared matches for the grandaughter 7.7, the whole family of 6 appear as shared matches, plus a couple* more descended from the same branch as the third cousin, also a couple more.
Looking at the same family from my first cousin's match list.
Third cousin shares 63 cMs with my cousin, considerably less than me.
Shared matches for third cousin, only 3 family members show up, three grandaughters don't appear.
My cousin is not a match at all with one of them. One other shares 8.3 cMs.
Shared matches for grandaughter 8.3, the whole family appear, less the missing match, plus the same couple*
Ancestry are really a law unto themselves. Without a chromosome browser there is no way of sorting out matches properly. Recent improvements (with the exception of Thrulines) have been very helpful, but combined with a browser they would be exceptionally helpful.
Regards Margaret