See also my post #6 above.
I have several 6cM or slightly higher matches in my tree, but most are marked as tentative. I would be wary of accepting a single 6cM match as proof of a specific relationship, even with paper or other records to corroborate it, unless you have investigated all subsequent intervening relationships in your wider tree. If you find several similar matches to a single MRCA or couple though, the chances are correspondingly higher that there must be some weight to the evidence.
But as an example, I was delighted last year to discover a new 6cM match, which on the face of it corroborated my research back to my Gx5 GF, as both I and my match were direct descendants of different children of that man, but my match by his first wife, and myself by his second wife.
Quite simple you might think. But one of the benefits of researching a tree widely and deeply is that I was able to see that there were at least three other local families whose members had at various times married into and become direct ancestors of either my match or myself. So in fact it is impossible for me to say with any certainty whether we share a match to my Gx5 grandfather, or one of the other families whose siblings appear in both our lines. One for example being my Gx3 grandmother, whose brother it transpires was also one of matches' intervening grandparents.
I have another 6cM match who descends from my Gx6 grandmother and her second husband on a different line. I am descended from the same woman and her first husband. But a direct descendant of the second husband's brother married my Gx2 GF and is therefore my Gx2 GM. So which line do we match on, either or both? It is impossible to say, or could the match just be IBC?