I agree the confidence level relates to the probability that you match the person with a relationship as stated even if they got the match wrong. Attached is a screenshot of a match found in my tree by ancestry for Adam Wylie. The match is for my maternal line which was done long ago and I am working on my paternal side. I sent this to my maternal cousin and he was at first excited because we cannot prove our relationship to Adam Wylie and likely this person cannot either.
If you look below the match, there is a list of other surnames. when I checked this list, I found another match in the Patterson line. Mu cousin was able to confirm this match as correct and is most likely the correct match.
Now if we had our raw data and could see which segments we matched, we might be able to verify this as a double match if I matched other Wylies on one of the same segment. Ancestry, PLEASE let us download our raw data.