Whilst it is perfectly possible that some 6cM matches will be correct, and can be corroborated by alternative methods, I would never rely on a 6cM match without additional corroboration as proof of a relationship.
According to my textbooks, at a match length of 7 to 8 cM, around 50% of matches can be expected to be false (identical by chance, by population, by state etc.) So the probability of a 6cM match being genuine is slightly lower than that, i.e. it is fractionally more likely to be false.
Think of it this way: Ask 1000 people to write down a random string consisting of four numbers. Then ask another 1000 people to write down a random string consisting of 100 numbers. The chances that two or more of the random 4-digit strings may be identical by chance are much greater than for the 100 digit sequences.
Because lower DNA match lengths are shorter, the same probability applies.
As the length of a match increases, the possibility of false matches decreases. It is generally accepted that at and above lengths of 16 to 20cM, matches can be considered reliable.
Bear in mind however that many shorter matches on Ancestry are given those match lengths after application of Ancestrys' Timber algorithm, which aims to strip what the process considers to be false match lengths from matching segments. That must decrease the possibility of some 6cM matches being false, but to what extent I don't know, and it is also possible that Timber may in some circumstances strip out genuine segments. You can check the unweighted match length for Ancestry matches at lower lengths, and if it it longer than the headline match length, it indicates that Timber has removed part of the original match. In those circumstances, the probability of the match being genuine may be slightly higher than it appears.
