Two holding one tallit

Today's lesson in Mishne Torah features a halacha found in the beginning of Baba Metzia "two holding one tallit." How does this relate to one's G-d service? "Tallis" here refers to  the encompassing light (Or Makkif)  which is drawn down through physical performance of mitzvos. And when two Jews fufill a mitzvah together, they both are holding the "tallis" and each one is claiming it is he who caused the drawing down of the hamshocha of light  and this drawing down is his alone. 

This has to  be understood: 

1. It's known that the most complete way of avoda is "not in the way of receiving reward" (Pirkei Avos). How is it then possible that each one will claim heatedly that the entire "tallis" is his? To the extent that he's ready to testify!?

2. Since after testifying and swearing neither one will be entitled to more than a half of the tallis, wouldn't it be benecificial for the both to simply split the "tallis" beforehand?


The explnanation is as a follows: They're not clamoring to receieve an extraneous reward stemming from the essence of the mitzvah  which is a command and a connection with the Essence and Being. And since this aspect is connected with their souls, it doesn't stand to reason that either one will yield his desire for his half!