TW,
Others may have a better explanation for this, but, as I see it, the basket will not be stable until the clutch is assembled. The double-row of ball bearings only hold the radial position of the basket. I think the basket can still teeter (so-to-speak) until the whole clutch is assembled and the pressure of the plates hold it in place. I may be forgetting something here (I have done that before while thinking I had the right answer), so I am prepared for being corrected.
by the way, I don't know if it is even possible to put the clutch hub in as shown in the Haynes diagram, because they show it backwards, as does the BSA parts book.
Richard L.