It is hard to know what the Mishna means.
So when we get to Ravina and Shmuel things pick up. Ravina says, all that matters is the "this," and Shmuel says all that matters is who said it (the person that wants to rent, or the one that wants to rent out his place).
Here is where the Rambam comes in and brings the Tosepfta (teaching) that says exactly the same things as the Mishna in the case of renting and says openly it does not matter if the word "this" was used. This is a proof to the Rambam that if the renter said it, then it does not matter. My point is it is hard to see why the Tospefta should be assumed to be a proof of the meaning of the Mishna.