Don't take other people's trees at face value. You need to rigorously investigate them to verify the information they contain with the same level of certainty that you have presumably applied to your own. People make genuine and honest mistakes. They make assumptions. Some also copy other peoples' trees or branches thereof in bulk without checking and verifying the information they add to their own trees.
Two people with the same name at a location where you might reasonably expect a common ancestor could suggest that one or the other of you might have made a misidentification. I've just spent a few hours looking at a My Heritage smart match I was notified about this morning. The other tree owner's family goes back to a man with the same name as my Gx3 GF, and he is shown as the husband of my Gx3 GM, but he was born 2 years earlier than my Gx3 GF, to different parents. I have been checking my tree and doing my own research on the associated people in the "matching" tree this morning, with an open mind. But the evidence I already have, including numerous DNA matches, and the information I have found in parish registers, censuses and other records for the family line of the namesake in the other tree have confirmed to me that the owner has misidentified the man - one of three men including my Gx3 GF having the exact same name and born within 6 years of each other in two adjoining villages.
DNA match lengths can vary greatly for most relationships. The Shared cM probability tool at DNApainter.com illustrates the range of match lengths that can apply to different relationships. All that sites such as Ancestry are doing when they say that a match is 2nd cousin, 3rd cousin or whatever are giving you a hint as to the most probably relationship between you based on the length of the match. But it is a hint, often the most likely of a number of possible ways in which two peole with the same length of match could be related, as the DNA Painter tool will show you if you enter the cM length into it and look at the results. The other relationship possibilities are just as valid, and whilst the most probable relationship makes it the most likely match, it doesn't follow that it will necessarily be the correct relationship for your match. Certain percentages of relationships at the same match length have to fall within the other probabilities, or they wouldn't exist!
So with every match you look at, it can be a slow and often painful process to work out the actual relationship. I am usually prepared to accept that my match probably knows the names and probably the year and place of birth of their own parents, perhaps even some or all of the same information for their grandparents. Armed with that information, if they are in the UK, you can usually start recreating and verifying their tree for yourself, in the same way that you would do, or have done, with your own ancestors.
I'm not suggesting that every or even most trees on Ancestry, FindMyPast etc. are wrong. There are a lot of good, well researched trees. but by verifying them - doing the research independently for yourself - you will confirm which are the good ones, and find the mistakes in others. If you don't, at some point sooner or later, you will get your fingers burned and you may not realise it until you have spent many more hours on research of your own before realising that you have gone down a wriong alley, need to unpick it all and start again.
It is also well worth researching your own tree to be as wide and deep as possible, certainly from the 1841 census and forward to as near the present as possible. So by that I mean researching the siblings of your grandparents, GGPs, Gx3GPs etc., their marriages, spouses and children, bringing each line forward to the present. With relatively high matches such as those you are dealing with, it is often then very quickly apparent how they fit with your family, as you will; find that you will often already have some of their ancestors already in your tree, their lineages confirmed.
I hope that all makes sense. DNA tests and matches give you information that can lead you towards certain probabilities, but other than parent and sibling relationships, they show you possibilities that can be filtered by degrees of probability to greater or lesser likelihoods of particular relationships, but you need to follow the paper trail through normal historic records to verify which is correct and confirm the match.
