The results say you're related. I guess there is some margin for error but I've never read what it is.
I and a lot of others have had our best results from the low confidence matches. Especially if your ancestors came to America during Colonial times.
The tree matches are based off of your and your DNA match's direct ancestors only. How accurate they are is determined by how accurate the two trees being compared are.
The surname matches give hints but you can't assume the actual DNA that matched is from one of those names. If your tree is like most of ours you're missing the maiden names of some of your GGrandmothers over the generations.
You'll have to decide how you want to handle private tree and no tree matches. I toss them in the trash myself.