One sentence, two different explanations

One hand washes the other, but together they wash the face

I've got two explanations for the proverb, and they seem contradictive:

A: It takes two hands to wash a face even though it only takes one to wash the other.
B: Working as a team lets you do things you cannot do alone.
(C's opinion seems inclined to A's: we can each support each other but it takes all of us to support the whole.)

Now it has been a standoff.