The Acharonim ask the very obvious question, how can the Gemara think to bring a proof from the Mishna, the Mishna is clearly not a case where you are picking it up for your friend. There seems to be 2 fundamental approaches:
1. The פני יהושע says that אין הכי נמי. The רישא in the Mishna is not מגביה מציאה לחבירו because you are not picking it up for him. The Gemara could have asked this and deflected all the proofs from the Mishna. However, the Gemara had other answers to deflect the proofs. למסקנה that we learn out from the last case, there is no problem since they both agree they picked it up together.
2. A person is assumed to have the necessary כוונא in order to acquire the object. Therefore, if in the mishna he needs כוונא for his friend then we ascribe that כוונא to him.
There is a מחלוקת the סמ"ע and the ש"ך and the קצות and the נתיבות whether by מגביה מציאה לחבירו the person who picks it up needs to verbalize his intent for the other person. The סמ"ע and the קצות both say that if Reuven is picking up for Shimon, Reuven needs to verbalize that he is picking up for Shimon when he picks up the object. The ש"ך and נתיבות disagree. It is pretty clear that the סמ"ע and the קצות need to learn the Gemara like the פני יהושע. If they hold in a regular case you need to verbalize, they would clearly hold in the Mishna's case that it doesn't work.
According to everyone the pshat in the Gemara's deflection from the רישא is as follows:
There is no proof from the רישא because maybe מגביה מציאה לחבירו לא קנה חבירו, however the din in the mishna will still be יחלוקו. Since they are both holding it and they both claim it is theirs, there are 3 possibilities:
1. It is Reuven's
2. It is Shimon's
3. They picked it up together and it is neither one's because מגביה מציאה לחבירו לא קנה חבירו
We will not let a third party take it because maybe it is one of their's and therefore the din is יחלוקו
The Gemara however, does not deal with the issue that how is this מגביה מציאה לחבירו if he didn't have כוונא to pick it up for him.