We find that common knowledge is sometimes used as a kind of testimony. This is even brought in the Shut of Rav Moshe Feinstein. There is a law about milk of a gentile. However because of  אנן סהדי common knowledge, Rav Moshe allows it. []Anything other than cow's milk would receive a fine from the government so it is a  case of "we testify"--common knowledge. But that can not make a marriage or a divorce as Rav Shach notes.  Even if we would have a case of a woman brining forth her divorce document in which case we would say that she received it in a proper way, still if witnesses came and said she found it in the trash, this would not be a case of two against two. 

So I suggest אנן סהדי common knowledge, is used a legal only in the case of a derabanan., not laws from the Torah.

[You can see how this is relevant when two people are married and then divorced without all the details of divorce. Then the woman remarries. Are the children of the later marriage mamzerim? I say "No", because of the above idea that the first marriage also did not have two valid witnesses.