So why then does Ancestry tell me a match is on my paternal side accompanied by a thru line to my maternal side? Or vice versa? Does not happen all the time but it happens often enough to undermine their credibility. Leaves me wondering - which bit is right?
They say their ancestral line labels are about 90-95% accurate, which I would say is about right. With much of the inaccuracy coming from lower cM matches.
The common ancestor matches are suggestions. They could limit them to when they only match the judged relevant sides of ancestry for both parties. But then they may not show them when their ancestral line predictions are wrong. Some people don't define the sides of Ancestry, probably about 50%, so that complicates things. And you can guarantee a minority have assigned the wrong side. It would be useful if Ancestry also told you the side of the match's ancestry they think it relevant.
I think that Ancestry only shows one common line of possible shared ancestry. While there are sometimes two or more. So they could perhaps show more than just one.
As with member trees containing a lot of errors and shared matches - the suggested common ancestors are a point of reference, which need to be looked into further.
It's much better they provide these tools and people make what they can of them, rather than not providing them at all. Just as most people don't know how to research using paper records and generate invented lines, people misuse the information provided via DNA matches out of not knowing the limits and pitfalls...
I've seen some people who have used DNA to construct invented lines. As one example, one group of my matches has a birth out of wedlock and one descendant has word of mouth information that the unknown ancestor was a Baron Leigh. They say they have found evidence of this in their DNA matches, but when I looked through their matches found it was a few wisps of a couple of the Baron Leigh's ancestral surnames in the 1600s. Another match has used DNA to fill in a dead end, where he found a single Patrickson match to his Patrickson dead-end and added the earliest possible ancestor from his match as his ancestor. My grandmother was born out of wedlock and Ancestry DNA suggested the entire line of her mother's later husband's ancestry as thru-lines. This owing to all ancestors living in a small area. So of my matches, various of them just happened to have ancestors that suggested this was my ancestry. But none of those matches with this suggested ancestry overlapped with DNA...
If you want to extract useful information from Ancestry DNA, it involves going through all the matches manually, considering how each overlaps with others, extending trees beyond what matches have listed themselves. The suggestions of paternal-maternal lines, cM levels, shared matches are clues which need to be deciphered. They could and should (for the price they charge for ProTools) provide more and better tools in this endeavor, but they still have the best system overall by a long way.
In the case of common ancestors, when you add a person to a tree on Ancestry, they check to see if they think that person has been entered in [an] other tree(s). Each person is assigned a unique identifier. The way they locate your thru-lines is by plugging your tree into their amalgam of all trees. Thus the suggestions rely on what users have submitted. There is no checking if what they have submitted is correct, as it would be infeasible.
There's a lot of stuff you need to know when working with DNA and then a lot of work to figure out how matches relate to you. What Ancestry can do by itself are useful time-saving suggestions, which may be wrong. As a few small extras I've found:
1) Sometimes there is no linked tree, but it you click through to the match's profile there can be public trees; or sometimes bios that are enough to piece together a tree yourself
2) Sometimes there is a linked tree, but it appears it has only one person in it, but above it says something like "tree with 1,456 people", if you click through to that, you often find a link somewhere in the tree
3) It's not uncommon to find linked trees when the wrong person has been linked, usually the spouse of the person who took the test; and that can sometimes be fairly obvious by comparing the ethnicity estimate, e.g. the linked person is half Italian, half British, while the ethnicity of the test states half Polish, half British; and that can fit the spouse of the linked person