DNA is accurate in proving relationships.
There is a caveat though, in that with matches sharing 10cM and lower can be false positives.
Statistically Second Cousins share DNA in the range 41-592cM which is very reliable.
Look up the Leeds Method, which is a cluster type method, it may help you understand more.
Alas not responding is typical of shared DNA matches, my first significant none responder shares 240cM with me and that took 5 years to resolve, he did have a family tree, him and his Dad but that was enough and that tree now has 1700 people who are either of Irish or Italian origins.
Is DNA evidence enough……well my counter argument to the doubters is that paper trails alone can be and in my own case very wrong. In my many GRO BMD certificates 3 are in error including my own birth certificate. I will only have DNA to prove that my registered Father was not my Biological Father yet my Half Sister and I share 1800cM so there is no doubt who was my Father.
DNA validating each branch in your tree should be the goal, for that means the tree is Biological as opposed to a Genealogical tree which relies only on documents and citations. A biological tree may or may not be accurate, for all it takes to be in error is the product of an unknown affair to be born and brought up as an offspring of a person who has no biological relationship to them.
Do look up the BBC Sounds series The Gift, there as two seasons of DNA stories. One tells of a guy who spent 30 years building his family tree only to find via a DNA test that he had no shared matches that he could resolve, he was adopted and never told.
Do read through
https://www.rootschat.com/forum/index.php?topic=863488.0