Shoshoni pine nut winnowing basket in use (photos from ISU museum). 

Why not make this a circular rim, as we see in the camus basket

1) The rose petal shape allows a more firm area (pointed end) in which the upward force of the toss can be transferred to the nuts, but the downward force of the nuts can be absorbed by the less firm area to prevent the nuts from bouncing out. 

2) Due to entropy, the nuts coming down will be covering a larger area than the nuts tossed upward, so a broader catch area is required.