Daf Yomi Yevamot 113b -- Two Different Types of "Knowledge"

A nitpick on the gemara:

Mishna:

העיד רבי יוחנן בן גודגדא על החרשת שהשיאה אביה שיוצאה בגט ועל קטנה בת ישראל שנשאת לכהן שאוכלת בתרומה
אמרו לו אף זו כיוצא בה
פירוש אף זו שנשאת כשהיא פקחת ונתחרשה כיוצא בה כשם שחרשת שהשיאה אביה שאף על פי שנישואיה נישואי תורה מתגרשת כך זו הפקחת שנשאת ואחר כך נתחרשה אע"פ שנישואיה נישואי תורה מתגרשת

Rabbi Yochanan ben Godgada testified regarding the female deaf-mute whose father married her off, that she goes out with a get, and regarding the female minor, daughter of an Israelite who was married to a kohen, that she eats of teruma.
They said to him: Even this one is like her.
{Yevamot 113b}
Gemara:

העיד ר' יוחנן כו':
אמר רבא מעדותו של רבי יוחנן בן גודגדא אמר לעדים ראו גט זה שאני נותן וחזר ואמר לה כנסי שטר חוב זה הרי זו מגורשת
מי לא אמר רבי יוחנן בן גודגדא דלא בעינן דעתה דאשה הכא נמי לא בעינן דעתה דאשה
פשיטא
מהו דתימא כיון דאמר לה כנסי שטר חוב זה בטלי בטליה קא משמע לן דאם איתא דבטליה לעדים הוה אמר להו ומדלא אמר להו לא בטליה והאי דקאמר לה הכי מחמת כיסופא הוא דקאמר לה

"Rabbi Yochanan {ben Godgada} testified...":
Rava said: From the testimony of Rabbi Yochanan ben Godgada, if he {the husband} said to witnesses, "see this get that I give," and then turns to her and says "take this document of indebtedness," she is divorced. {since a woman may be divorced without her consent, or in this case, knowledge}
Does not Rabbi Yochanan ben Godgada say that we do not need her knowledge {consent}? So too here we do not need the knowledge {here, actual knowledge} of the woman.
This is obvious!
I would have though since he says "take this document of indebtedness," he has canceled it {the get}. Therefore it informs us that is he had canceled it, he would made a statement to that effect to the witnesses, and from the fact that he did not make such a statement to them, he did not cancel it, and this that he told her as he did, it was to conceal his shame that he said this to her.

Rather than make such intricate distinctions and explanations of the man's intent and the meaning of his statement, or his inner motivations -- which surely is not what Rava intended -- we might say: Rabbi Yochanan ben Godgoda was speaking of a woman with Biblical marriage who could be divorced despite being a deaf-mute. This is because divorce does not need consent, and thus does not really require her knowledge of the matter. Thus, Rava's derivation that the husband may even mislead a normal woman is a fair derivation. But it is not necessarily so obvious, as the gemara states. There may be a difference between lack of knowledge/consent and false knowledge of what is going on, after all. Rava is saying that there is this equivalence.

No great chiddush here, but still something to point out.