The interesting thing is that apparently the Rif and Rambam both said that R. Elazar who said עדי מסירה כרתי [the witnesses that see the giving of the document cause the divorce to be real] really meant אף עדי מסירה כרתי [also the witnesses that see the giving of the document cause the divorce to be real]] which is a surprise to me. [R. Meir said the witnesses on the document cause it to be real and valid. So the argument is only in that R Meir disagrees with R Elazar. But R Elazar agrees with R Meir.]
[Not that I ever learned that tractate very well anyway.] In any case, I saw Rav Shach brings up the larger subject of what constitutes any valid שטר (document). And he says that a valid document to be valid at all needs witnesses. But כתב ידו [one's own handwriting] also counts as a valid document.
That is he says that famous Rambam about a document that says שדי קנוי לך ("My field is acquired to you") is valid even with no witnesses- is talking about כתב ידו (handwritten).
This is what leads to the famous practice in Litvak yeshivas that when someone asks for a loan, they write a small note, "I owe you $10." (for example). [That practice is based on two principles. (1) One should not make or receive a loan without a document or witnesses. (2) The other is כתב ידו (a handwritten document has the category of a valid document) is מחייב (obligates).]