"Should I just leave it there? and not tell him that the research is absolutely riddled with holes. Is ignorance bliss??? Would you want to know?"
As others have said, in this particular case, I think that it would likely be better to just leave it be.
"I did try and ask him his source for one particular ancestor but he just sent me a link to a marriage record that doesn't connect / prove anything"
But, if you did want to question him further then this may be a good starting point. Appear innocent and naive and seeking guidance.
"Thank you first cousin once removed (so either they are the child of one of your first cousins or one or your parents is their cousin), that was very interesting. But I'm very new at this and I can't quite see** how that fits in with the tree. Would you mind explaining it to me a bit more?"
That will hopefully persuade them to explain why they believe that and you can then gently dig away at that strand and show them the error in their ways.
Either that or you can just ignore them and get on with your own research.
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Having said all that though,
"a link to a marriage record that doesn't connect / prove anything"
Did you have a read of the actual record or just the transcript. Ancestry transcripts can be wrong. Sometimes the transcript has totally the wrong name so you always do need to check the actual record.
But, if the transcript is correct then I would suggest either question them gently on that or just politely ignore them from now.
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"I'm very careful in my work and confident at searching resources etc."
I really do wish that I'd been more like you when I first started out. I like to think that I have got a lot more careful in my research now but some of the things that I just accepted when I first started out just make me cringe now.
"Oh, everyone else says that this person is the father so it must be correct" I have since learnt is definitely not the best way of proceeding.
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"Is ignorance bliss??? Would you want to know?"
It depends; ignorance may be the best way in the case of your cousin.
As to myself? I have learnt that I am very fallible indeed, so if somebody approaches me and points out an error then I am very glad to alter my tree to reflect that.
Although, frankly, it's mostly me going back over what I did originally and finding some pretty basic errors. But, I will say, that one error I found did have a pretty big impact on my tree (it was a 4xG grandparent born in the 1810s, so 6 generations back).
"I can't always trace the correct ancestors myself but I have uncovered information which shows the ancestors he has named are just not correct."
This is what I found. The people who I thought were his parents I now know were not his parents but I cannot find out who his actual parents were.
But, I have multiple DNA matches through that line. So he is definitely related somehow to the people who I thought were his parents, it's just that they weren't his parents (perhaps they were aunts/uncles or cousins once removed etc).
So, I'm not going to delete that link at the moment (even though I know it's wrong) but I'm going to carry on looking for what the actual link is between that person and the multiple DNA matches that I have through that line.
Have you done a DNA test with Ancestry? If not, then I would encourage you to do so.
Even more, I would strongly urge you to ask your parents (if they are still alive) to do DNA tests. The reason I say this is that they are a generation older than you and so have more DNA from older ancestors than you do and so you can link back further.
Both my parents have done DNA tests on Ancestry and they have so many more DNA matches than I do (and I'm certain that they are my parents).
Combining DNA information with traditional genealogical records really can help to solve a lot of problems.
This may provide an answer as to the accuracy or otherwise of this document.
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**I can't quite see - Sorry, this is a very obscure reference:
Guide to Maths Masters
'Sir i don't quite see this.'
nb it is essential to sa you don't quite 'see' sum as this means you are only temporarily bafled by unruly equation and not that you don't kno the fanetest about any of it.
Willans, G. and Searle, R. (1953) Down with Skool! London: Max Parrish & Co