I went back to have a look at the old Shared Ancestor hints with a couple of thoughts in my mind about why certain Ancestors may have a "Shaky Leaf" but not a "Common Ancestor".
I had two suppositions - that since ThruLines only goes up to an individual's 5th great grandparents, that any Shaky Leaf hint with a linkage above 5th g-grandparents would not get given a "Common Ancestor" hint (reasonably easy to test, two of my tests had "Shaky Leaves" for 7th and 8th cousins, linked through g-grandparents higher than 5x) and the other of course is that if someone has a private tree which is also unsearchable, they will show for a "Shaky Leaf", but not in ThruLines, as that relies on the private tree still being searchable.
And I found exactly what I was looking for- while adding "SL" comments on the notes I had made for each person with a Shaky Leaf hint, I came across three people who I thought would not have a "Common Ancestor" all of which suggested a link above 5x great grandparents (I wrote the specific relationship in the note, so I retain that). A couple of the results are shared across my father and paternal grandmother's results, but for both in the range of 7th-8th cousins, and one from my paternal line for my father with a 7th/8th cousin link. And when I turned the beta back on and went to have a look, none of those 3 test results came back with a "Common Ancestor" link.
As for the second theory - private and unsearchable trees, it's harder to prove, but I also had two Shaky Leaf hint matches both with private trees who do not appear as "Common Ancestors" where the link is 5x g-grandparents or lower. As I have a few "Common Ancestor" suggestions with private trees and I can see where the link is thanks to ThruLines, I assume that those two results have kept their tree unsearchable.